If your 2003 VW Gti gets overheated and the motor cuts off the fuel so you cant go anywhere does that sound like a thermostat problem or water pump And if not that what?

I just encountered this problem with my GTI. But I haven't got it hot to a point where to fuel cuts out then car wont start. I took it to the shop and help diagnois the problem. I was told that its really common for the water pump to fail in the 1.8t mk4s. So i just went ahead and got the water pumpreplaced plus the timing belt and the thermostat. I hope that this info helps you. (78,000 miles)