The real reason !
Dispite the talk of thermosomething valves the real reason for "walming up" the transponder it the mode C encoder works at a constant temp and to do this it is fitted with a small heater and this takes time to get up to the correct working temp.
Next time your aircraft is in the sheds for the radio annual check if you watch the transponder check you will see that the mode A code works almost instantly but the mode C will drift around for about 5 min before reaching a realistic reading.