I can tell you come from a nitro background!
Firstly, we don't tend to gear by temperature. Rule of thumb is that if you can't hold a finger on the motor for more than a couple of seconds then it is too hot.
As a wild guess, anything over about 80c/176f is on the hot side. You are very hot.
Second, spur/pinion sizes mean nothing without the internal ratio. We need this to determine the overall ratio.
Third, cars don't race up and down streets with the body off so it is not a realistic test.
Personally, I would be looking to gear a 9 turn brushed motor starting at around 7.5:1 overall on a medium outdoor track, and more like 9.5:1 indoors.
Sounds like you need to go down several teeth on the pinion.