My car’s temperature gauge will go to hot if I sit at a stop light or have the car in park. Also, it blows cold air out of the vents.
Overheating: Another item to check, as well as the below mentioned, would be a stuck thermostat.
If it is stuck closed, coolant only circulates through the engine and never reaches the radiator where air passing over the radiator cools the coolant.
The reason why it overheats at standstill is because there is no air moving past the motor.
To check for a stuck thermostat, run the car until it warms up, when/if the fan kicks on the thermostat should be open, touch the upper radiator hose and see if it feels cool. If it is, then the thermostat is not opening.
Check that the fan is working properly.
I had the same problem on a car I previously had and noticed that the fan was not working.
Check the coolant level.
Inadequate coolant can not reach and flow through all engine coolant passages. This causes the engine to run hotter than it should.
If coolant is not filling the engine passages and heater components, it will not flow into and through the heater. Air blowing from the vents may be cooler than it could be.