Hi,

I want to say be suspicious of the sending unit or the wiring to the gauge may be going to ground in like a frayed wire inside the harness.
That wire can get powered or be grounded through another source.

The top hose and the radiator itself should be hotter at the top as heat rises and the water is less dense.
The bottom of the radiator should be cooler as it loses heat and the water cools. It goes downward by natural convection.

So with that there is a conviction about a dead pump or sensor and or gauge.

You really have an infrared thermometer for occasions like this
They are also handy for reading brake disc and a myriad of other things besides a car.

Just saying both conditions of a spun pump impeller or a wiring issue comes towards you as being uniquely rare.

Phil