The Bowden cable lets the transmission know how far you have pressed the accelerator pedal. At lower speeds, pressing the pedal down, but not all the way, will not activate the kickdown switch, but will let the transmission know that you are accelerating. Depending on pedal position, gear and rpm, the transmission will downshift, or stay in the same gear.

If it is adjusted too 'sensitive' it will fool the transmission into 'thinking' that you have the pedal further down than it actually is, and may cause premature downshifts with less pedal travel.

You may want to adjust the cable housing in the opposite direction, so the cable does not move as far, if that makes sense. That should mean turning the adjustment of the cable housing so the housing gets 'shorter', or not as many threads are showing at the adjustment bracket. Be sure to loosen the locknut first, try 1/2 to 1 turn at a time and see what happens.

Of course, it could be something else internal to the transmission that is affected by heat...

Let us know.