Don't know much about VW engines but when I had this problem on a Citroen I suspected it was a worn HP diesel pump which I changed and it cured it but it subsequently turned out that it was not the pump but the pressure regulator on the pump that was causing the problem.

Don't know if yours is a common rail engine, the Citroen one was, if it has an injection pump that could be the problem as the fuel being less viscous when hot may fail to reach the required pressure, but it could as you say be a sensor causing the problem.