Temp gauge doesn't seem moving heater blowing cold

Hello,

If the temperature gauge shows engine is cool and the engine is not warming up, it could be due to a stuck open thermostat.
When a thermostat fails, it can fail in one of two ways. It can fail at stuck closed position (lead to overheating), or it can fail at stuck open position (engine will not warm up).
When it fails at stuck open position the coolant will circulate thru the system and will not allow the engine to reach its operating temperature. Which leads to the heater not blowing hot air as it is designed to do.

Here are couple of helpful articles:

https://www.2carpros.com/articles/how-an-engine-thermostat-works
https://www.2carpros.com/articles/replace-thermostat

Please let me know of any questions.
Thank you.