my temp gauge is in red when i the vehicle is completely cold

What is your question?

so i notice my temp gauge was reading red and the engine overheat signal came on. i immediatley pulled over and had it towed to a land rover dealership. they said it was my thermastat that went bad and it would cost 600 bucks. i obvioulsy said F that and replaced it myself. Well the new thermostat is in and ould one out but my temp gauge will go from blue to red when i start it. so i left it running for about 15 mins to let the new thermastat kick in and start doing its job. Well of course the temp gauge didnt move. Here is the kicker to this. I turned the ignition switch on this morning without turning the engine on and my temp gauge went from blue to red. I have no clue what the heck is going on now. Any advice would be awesome.