Most probably your DME relay, they can create interminent fault which can be
sensitive to temperature.
This is because the spring loaded contact inside can get weak and the
contact points will burn, this will also happen if you try to start the car
with weak battery.
First think you need to know that the function of the DME relay is to turn
on the fuel pump WHEN the engine starts cranking ( on 968 it also turns on
the idle stabilized circuit and O2 sensor but that may not apply depending
on the age of your 944 ). This is a safety feature, when your engine stops,
so does the fuel pump.
The way it works is that pin 30 of the relay is always on, connected
directly to the battery. The DME computer detects the engine cranking it
grounds pin 85 of the relay which then switches power to pins 87 (pump) and
If necessary you can take the DME relay out, connect pins 87 & 87b to 30,
you would her the pump run and you can start the engine and the car will run
normally. Sometimes the DME computer no longer grounds pin 85, in which case
you can wire 87 & 87b into the ignition circuit (the auto tranny fuse is
good for that even if you haven't auto tranny).