It's getting air in the system.

The fuel filter has a temperature valve whereby if the fuel temp is below 40 degrees, the leak-off fuel from the injectors and HP pump returns to the filter and is re-used once it passes through the filter again. Once the fuel temp rise above 40 degrees the valve opens and this fuel returns back to the tank for cooling.

It might be there is air getting in the leak-off side, so clear hoses need to be fitted to check for presence of air.

It could be the same things as I had where the seals in the pump had gone hard and were letting in air when cold, but sealing up when hot.

I had a bill for just under £800 to fix it, but mine escalated to the stage where the EM light was coming on and the engine would cut out.