Citroen c4 coupe car wont start when engine is hot/starts fine when engine is cool or cold have changed starter motor fuse no change

A couple of possibilities. Since they probably disconnected the battery to replace the starter, they may have left a feed wire to the fuel pump circuit disconnected when putting it back together They may have accidentally grounded a circuit and blown a different fuse. You need to check fuel pump pressure to see if the pump is putting out enough pressure. The pump just may have just wore out and cannot feed the injectors. Air may have entered the fuel system and needs to be bled out.

I don't know what testing you have done, as far as wiring circuits? You can see the starter fuse in the diagram, not only check the fuse, check for voltage on the fuse circuit, use a test lite to check for voltage. At the starter motor itself, two voltage circuits, one hot all the time, the other goes hot when starter relay is energized. Check those voltage circuits. The starter motor grounds through engine block.
You can unplug starter relay, use proper jumper wire, between terminals 30 and 87, the starter motor should crank the engine. If you try that, make sure tranny is in park or neutral and parking brake is set.

the coolant temperature sensor is fitted in the thermostat housing which is bolted to the side of the cylinder head (gearbox side), to locate it follow the top radiator hose, if i remember correctly the sensor has a green connector

i had an old ford capri that did this in the end it was a dodgey starting motor i changed this and it was fine take it to a auto center and get the battery checked any way but it sound like a starter to me

Starter motor fuse
http://www.aev.com/uploads/file/SPRINTER%20NO%20CRANK%20NO%20START%20.pdf
See Mercedes letter.
Takes 25 amp.

the gearbox will need to be removed and the clutch inspected it sounds like the drive plate is unservicable

The problem is with the starter assembly. Replace the starter, and the problem will be over.

check catiletic convertor

As far as I know when a car does not start when is hot the first thing I check is the Compression, second do the Valve clearance.Try it.

If you check your engine fuse box and find that your 20amp fuse is blown its either a sticking starter relay or water getting in your electrics. Try checking this first as the fuse box is directly above wheel arch and can get damp. Clean up green contacts and keep a spare 20amp fuse handy. After changing this blown fuse you will need to reset the engine management system by disengaging the battery terminal. You're clocks might be out but car will now start. Don't forget to buy that starter relay if problem persists.