Making this cat toy for my cat. The new motor works well but this rail on the back of the battery well heats up under load

So I've gone through a few variations of this, those three double A's are up putting 4.5 volts and this new motor is just about that and a little stronger than that smaller one. That was my previous motor that you see in the back. It's working pretty well when I have the cat toy on there. It's going pretty steady and I'm not getting too much heat from the motor like last time, though the battery rail on the back of that casing heats up quite a bit. Do battery rails usually heat up this much and I just don't see it because they're not usually exposed.?

I let it run for a bit just to see how bad it would get and it's not damaging the plastic or anything. It's just pretty hot. How much of a concern do you think this should be? Keep in mind this is going inside of a cat scratching post that is more or less just cardboard so I'd like to iron out any kinks before I install it