I'm not sure what the actual complaint is here. Is it overheating? You have heat from the heater core, so it seems like the thermostat is working? The temp gauge is reading the radiator temp and not block temp so it often won't show the problem until things get pretty bad. The fans won't come on unless that switch gets hot and since the water is cold near the bottom, (at the fan switch?) they won't come on.
Do the fans come on when the AC is on? They usually come on as soon as you engage it.
I've seen folks make the super easy mistake of getting the thermostat installed backwards such that the actuator isn't on the hot side, so you might want to check that. I've also seen a bad NEW thermostat that refuses to open all the way. Removing it and testing might isolate it in either of those cases. Note that running without one will result in a cold heater and less efficient engine so if that is it you'll want to fix it proper eventually but removing it will rule it out. You've probably noticed they like to overflow with the top off. If it's got no movement with the top off, that also points to the t-stat.
Hope my rambling helps somehow.