97 Toyota Tercel temperature gauge always up, heater blows cold

I just bought a 1997 Toyota Tercel 5-speed stick, with 175,000 miles, and the temperature gauge moves from its lowest possible position to its highest possible position when the key is turned on, although the engine does not overheat, and no coolant is leaking or being burned. I replaced the coolant temperature sensor, but the actions of the gauge were not affected. I don’t know if it is somehow related, but the heater blows cold, regardless the setting of the temperature dial on the dash.

Can anyone tell me what I might try next?

Thermostat, plugged up heater core, bypassed heater core, shorted wires, bad cluster. Just to name a few.

Do you mean that first thing in the morning, cold engine, the gauge reads hot as soon as you start?

Check the fluid level in your radiator when the car is cold. Not the level in the overflow tank.