cold Megane immobiliser problem

This may have been covered somewhere before but I have searched and searched, so easier to ask!

I have a W reg Megane Alize hatchback who i love dearly and runs like an angel. Sailed through her MOT, then stoppped turning off the immobiliser for me.
BUT only when the temps are low.
So if the car is in a warm spot, the immobiliser will turn off.

Scared to take her out in the sun cos as the day goes on the temp drops and if I turn off the engine, she won't go again in the evening chill. Got stranded in town and slept at my daughter's house after calling the RAC who didn't know what was wrong, and hey presto! the car started fine the next morning in the sunshine.