Not true.
I have run mine down to next to nothing (under 5L) fuel temp stays the same the whole way.
A while ago I had a thread and argued the fuel cooler was more of a fuel heater. I don't think it was conclusive but I did agree that it's easier for fuel mapping if fuel temp is constant.
The fuel cooler that is actually a heater will heat the fuel to about 70 degrees from memory about the same time the engine reaches operating temp (about 75 - 82 degrees).
You can monitor and record the fuel temp with Nanocom
Happy Days

