Where is your temp gauge sensor located?
Do you have a thermostat? You shouldn't have one! What you are describing really sounds like there might be a thermostat installed.
Do you have a gate valve on the cooling port of the jet? Or a ball valve? Is it open?
Do you have a pressure relief bypass? Is it functioning properly? I'm not a fan of these because they deprive the engine of water. They also get lodged open with debris, starving the engine all the time.
What size are your cooling lines?
Are any of the lines pinched under the oil pan?
How are your cooling lines routed? Basically, you should have something similar to the following routing:
Jet pump cooling port => tee => water pump ports on block => through the block, front to back => through the heads, back to front => from the front of the intake manifold overboard.
It should be pretty easy to pull the cooling line off at the jet and connect a garden hose. It should only take a few seconds before you see water flowing out of your overboard dump.
If everything seems fine until this point, you would need to pull the bowl and check for obstructions to the cooling port. I have seen an instance where the wear ring insulator started pushing out and would cover the cooling port. This would only restrict flow in one direction, so blowing air or water back through the lines didn't reveal anything.