warm starting problems

[almost athletic]

My 1996 Audi a4 will start as normal from cold eg first thing in the morning and sometimes on short journeys ( no more than twenty mins) but when its hot I get nothing from the key it doesn't seem to take power when trying to start eg lights doesn't dim and stereo stays on but it will bump start fine indicating to me it's not an mobiliser fault??

Any ideas could it be the cts saying the temp is wrong preventing the engine to crank or possibly a relay between the key and starting motor

Any help is appreciated thankyou