Location of temp sensor coolant gage

The sending unit is located on the engine. I can't tell you where, because you didn't indicate what engine you have! There are several choices for a 2003 E-250. However before doing that, it's best to utilize a high quality diagnostic tool that can monitor component operations to see what the current sending unit is reading, relative to what the temperature is actually measured to be, verses what the gauge says to see if you can troubleshoot further and drill down to the actual cause of failure.

Turn the heater on - got heat?