Peugeot Repair Questions? Ask a Mechanic for Answers ASAP
This could be a wiring issue as things tend to expand when hot and its possible a poor or partial electrical connection is being pushed apart on one of the major sensors so check the connection plug and wiring to the following;
Crank position sensor
Cam position sensor
Throttle pedal position sensor
unplug each in turn and use some switch / contact cleaner spray on the pins to ensure its all grease / dirt free
Also worth checking the connections to the fuel pump for the same reason - unplug each in turn and give them a good squirt of switch / contact cleaner - Not WD40
and also unplug and inspect the main power relays and fuses for signs of overheating or corroded terminals - so the ones for the ECU and the fuel pump
And also unplug the wiring loom connections in the engine bay one at time and inspect for corroded or recessed pins.
OK if the wiring doesn't help then also check the connections to the EGR valve, if either the vacuum pipe of electrical connection are damaged / corroded then the EGR can be on all time which certainly will hurt performance. Its also possible that its a fault with the EGR valve so its worth removing the valve and cleaning it out with brake cleaner, if it looks particularly clogged then replace it.