The difference between hot and cold is telling you lots of things, it probably not a leak in the system otherwise it would be a pig to start when cold as it lets more air in the longer it left, probably not (leak back) diesel leaking back to the tank
In my experience its loose tolerances in the diesel injection pump as it expands with heat, to test this have some cold water when you get home and poor it over the injection pump to cool it down then try to start it, if it starts when hot better
then this might mean the pump needs replaced or rebuilt to bring the tolerances back down into spec - its a 5min check that will tell you if it is or isnt the problem then you can start looking to leaks in the system etc
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