A car that is reluctant to start first thing in the morning but then starts fine after that initial start-up could be a victim of worn engine internals. Specifically, if the valve guides or piston rings are worn enough, the engine may not have sufficient compression to fire up from dead cold. That fact that the engine got very hot at some stage is also a good way to damage things like piston rings and lead to the symptoms you’re describing. Pull-starting with, I presume, another vehicle can spin the engine faster than a starter-motor will, and for longer, and this could be enough to give the engine the encouragement it needs to fire up for the first time. Is the engine burning oil? Or blowing blue smoke? Both are signs of a worn out engine.
Other possible causes are many and varied and include incorrect ignition timing, out-of-phase valve timing, poor fuel pressure, the cold-start enrichment mechanism not working or a range of sensors not playing the game. And plenty more.
If your car was a V200, then I’d suggest that the diesel engine’s glow-plugs had failed, but the V240 was petrol only. But that in itself is interesting because the engine was more or less an older-design Mitsubishi built under license by Great Wall. As such, it’s a fairly simple old thing with not too much to go wrong.
Perhaps there’s a clue in the fact that the doors lock themselves as soon as you’re on board. Maybe this has something to do with the body computer (that controls functions such as the central locking and immobiliser) which should perhaps be talking to the engine computer, but isn’t first thing in the morning. Do changes in the ambient temperature change the car’s habits? Is it harder to start on wet days? Is the tank full of very old fuel? All these things can have an effect on a motor that is a bit cantankerous to begin with.