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Murphy's_Law
Probably not.
In your problem, you can essentially disregard the rim size for most purposes, since the difference between the tyre radius (the lever trying to turn the wheel) and the brake track radius (the lever trying to stop it) is only a small fraction of either dimension.
The problem with small wheels is rarely the slight difference in heat capacity, it's the moving of the tipping pivot to a lower position, which lowers the limiting deceleration before you endo.