[RedDevil]

The problem needs to be something that gets cooled (by air or fuel) during operation but gradually heats up from the residual engine heat.
The fact that it starts easily within 15 minutes seems to rule out anything mounted directly to the engine block, as that would heat up immediately.

How's the heat under the hood?
It could just be that the engine is losing heat somewhere like when you have a hole in the exhaust manifold (mine rusted through at some point), a leaking gasket or a missing heat shield (mine dropped off but was salvaged and refitted) or such.

I measure intake air temperature continuously by a cheap digital in/out thermometer. I've stuck the probe in several places under the hood to check temperature in that region, you could do something like that too and see whether there is a direct relation between temperature and your problem or not.
(My thermometer sadly does not give readings above 70C. I cannot use it for testing coolant temp etc. A high upper limit is something to watch out for when selecting a thermometer for these causes).