It sounds to me like the heater core is out. Have you noticed the floor wet recently? that's a sure sign of heater core issues. The other option is it will act like that if it has no antifreeze or water in the radiator, in other words the radiator is dry.
Just a suggestion if someone has replaced the thermostat its possible they installed it pointing in the wrong direction this could account for cold air and the guage reading over hot. , EzForJesus
I would suggest replacing it.
Usually at the firewall either passenger side or middle follow the heater hoses
under the dash right hand side.
To change the heater core in a 1987 Pontiac Sunbird, start by disconnecting the battery and draining the coolant. Remove the dashboard and the heater assembly to access the heater core, which is typically located behind the dashboard. Disconnect the hoses attached to the heater core, remove the mounting screws, and replace the old core with a new one. Finally, reassemble the heater assembly, reconnect the hoses, refill the coolant, and reconnect the battery.
The water pump pushes the coolant through the engine block and head(s) then into the heater core.
You can get a heater that magnetically sticks to the pan and warms the engine. You can get a heater that connects to the heater hose and circulates warm engine coolant. You can also get a block heater that replaces a freeze plug. You have to decide which works best for you.
i replaced my heater core and it has been fine ever since (8 months )
No, a clogged heater core will not make it overheat. A leaking heater core will.
there should be 2 hoses going into that firewall for the heater core, it is probably bad. find the 2 hoses and connect them together until you can repair the heater core, at least it will be driveable. one end of the hose attaches to where the top radiator hose connects to the motor, and the other end is on the water pump towards the bottom of the opposite side.
To replace the heater core in a Pontiac Sunbird, start by disconnecting the battery and draining the coolant. Remove the dashboard, which typically involves taking out screws and bolts, and then disconnect the HVAC controls and wiring. Once the dashboard is removed, locate the heater core housing, disconnect the hoses, and unbolt the core. Install the new heater core, reassemble the housing, and put the dashboard back in place before reconnecting the battery and refilling the coolant.
A leaking heater core will cause the engine to overheat because the coolant is leaking out.
check the heater core