Which one is more energy/fuel efficient to cool the inside of the car: lower thermostat + lower fan speed, or slightly higher thermostat + higher fan speed?

Mythbusters did a test on this comparing AC to driving with the windows open. The AC barely affected the fuel consumption, while the additional drag of open windows made a huge difference.

So because the difference between off and full blast is negligible, less than the wind resistance of open windows, I'd say it probably doesn't matter what setting it's on. Go ahead and blast it.

Likely doesn’t matter. Like. At all.

Ac is likely chilled to a given temperature regardless of what the final temp is called for.

The air is cooled by blowing it over a radiator on the cold side of the AC’s compressor, the radiator then absorbs heat from the air (putting it into the coolant.)

As long as you’re not putting more heat into the coolant than the chiller can extract, it’s only going to remove so much heat- more if it’s slower, because it’s in more time, it then it’s spread across less air, if that makes sense.

Regardless, the way temperature is controlled is by mixing it with additional ambient-temp air. (Either cabin air or outside air.)

So technically, it would be most “effecient” to have full cold, but (as already said,) the ac system is effecient enough it basically doesn’t matter.

Going the other way doesn’t matter at all because it uses waste heat from the engine in a bypass loop. That said, if you have a cold car you’ll slow down the engine warming up by turning on the heat. (You can see this when it’s very cold by warming up the engine and watching the temp gauge when you turn on the air.)

EVs are a bit different- heating from cold start is done with electric heaters. Once the car is moving and the motors are hot, they typically use waste heat from there.

I assume there’s little difference between ice and ev in cooling,

I think the more energy efficient will be the second option since you're not cooling to as low of a temperature. The fan speed change doesn't seem likely to be a big energy difference, but not having to cool as much is likely to save significant energy.

I'm thinking higher temp will cause the AC to cycle less, hence less frequent load on the engine and fuel savings

The one detail I haven't seen in the other comments would be to recirculate the air inside the car, so the car doesn't have to cool the hot air from outside, but instead only cool the already cooler air from the inside. To be the most optimal if your car has been in the sun you should make it draw air from the outside until it's a little cooler than the outside then recirculate

Older cars, the air conditioning was simply true false.

As in it was running or it was not running. You adjusting the temp warmer, just mixed more warm air into the chilled air.

I do not know if modern cars work that way.

If that's the case lower temp because higher temp is just adding warm air to your cold air.

But then we get into how fan blower motors work. Again, in older cars (I don't know how modern computerized cars work). The blower was on or off. The fan speed knob was actually a resister that caused the fan to blow less hard by reducing the amps to the fan. I'm not an electrical engineer, but I gather the lower speed setting is consuming the same amps, but turning some into heat.

IMO crank it. It's the same cost no matter the settings.

theoretically the most fuel efficient would be not having it on at all.

But it really depends on how vehicle refrigerant phase change loops work. I'm not a mechanic nor am i familiar so hopefully someone else can chime in?

There are a few outcomes here depending on the cycle. If it uses some sort of refrigerant flow restriction that is variable, then theoretically the thermostat setting will have an effect. (i would assume this is a case these days) However the effect it will have is not going to be linear, given that its a fluid pump cycle. Though it's powered directly by the engine (most likely?) so that probably won't matter at all, engines are horribly inefficient to begin with.

if it's not using some sort of variable valve to control restriction and thus cooling potential, it's doing some other shenanigans and running the phase change at a set point, though it would have to introduce some sort of external variable there in order to compensate so probably not.

I would probably set the ac to a low temp, and then the fan to a low speed, because it takes advantage of physics better that way (the greater the difference in temperature, the more effectively you can transfer heat away from it) since you're running a low fan speed, you're gonna need a high temperature gradient to make the best use of that. There is also the inverse, but i doubt that would be better tbh.

Though i think realistically, it just won't matter enough for you to bother. Like you'll probably see a bigger difference in usage by taking a different route somewhere, or idling longer. There are a number of other factors that can impact fuel efficiency.

There is some optimal amount of thermostat vs fan speed. Whether you're better with a lower thermostat and higher fan speed or vice versa depends on which side of this optimum you're on. We as random internet strangers have no way to find this.

It depends on a large number of factors. Largely it doesn't matter.

What I personally do is start my car with a low fan speed, let the evaporator cool down, then start cranking up the fan speed so I feel the cooler air. When it's really hot out my AC can't keep up in my car, and blasting the AC essentially guarantees that I'll never feel cold air. I'll just have a cooler ambient temperature, but the air blowing at me (that I'm feeling) is warmer so I feel hotter.

i'd guess that the A/C is the most fuel burn-y thing of the two.

i'd set the thermostat slightly high and turn up the fan.

your sweat evaporating has a cooling effect, and moving the hot and humid air away from you is what enables it.

There's a few things a bunch of other commenters are getting wrong, at least from my understanding.

The AC compressor is run by a belt from the engine. Unlike a home AC, a vehicles AC is either on or off. There is no cycling. The temp control is just changing how much outside air comes in, or how much heat is drawn from the engine.

The fan speed is not going to effect anything at all. The alternator spins to generate electricity to recharge the battery, but the amount of energy required to spin it doesn't change based on how much electricity is being drawn.

Tamping your AC down in any way, whether by lowering fan speed, or increasing the temperature is less efficient. Use it at it's coldest temp and highest fan speed if you're going to use it at all.

Edit: I almost forgot to add that AC efficiency is going to be more closely tied to your driving speed and outside air temperature. Driving faster makes your AC more efficient (not necessarily your whole car). More air passing over the evaporators means more heat released from your AC to the outside, which makes colder air in your car. The colder the air outdoors, the more heat the AC can release to the outdoors, which means colder air in your car.

As for EVs, I have entirely no clue, but I would assume it's a similar situation.

Edit: I may be entirely wrong. I'm not sure about anything anymore. I know a guy who knows all about these things, let me get him down here tomorrow and we can go from there.

Edit 2: I meant to make an edit and accidentally deleted my comment. I actually did meet with my guy. Im also too tired to work a phone. Can't wait to share what I understood from what my guy said.