aint just the heat of the light bulb is it?
have you checked the oil level in the gearbox,if its low/dry your gearbox will get hot,and worse could end up seizing up,if oil levels ok its probably just heat getting pulled through from engine as your drivinghi mates...im a bit skeptical abt the warm/hot feeling around the auto gear lever/knob whenever im driving her...is this normal or something is wrong ?...thanks in advance....
Also check all your earths.
I would have thought ambient is a bit hotter where you are than UK!
If it is the bulb might be worth checking it's the correct one, i.e someone hasn't replaced it with a side repeater bulb