Manual heating system with automatic trans. 7.3 L Diesel, 45k miles

Firstly, a thermostat that opens quicker will not give you better heat. Your heater core may be partially plugged causing a low flow issue. Another area to check would be the water pump impeller for corrosion or slipping on the shaft. Does the vehicle's cooling system operate well otherwise?

Could be air in the cooling system , try an bleed the system . On top of the thermostat housing is a bleeder valve , with the engine up to temp. open valve till coolant comes out . Is the coolant full ? What color is the coolant ? Have see where coolant turns like a muddy color an clogges the heater core an engine coolant passages . Check the heater hoses going into the fire wall ,are they hot ? Does your grand prix have manual or automatic climate control ? Duel zone ! Do you hear a clicking sound behind the instrument panel ? Bad temp blend auctuator .

It sounds like a heater cord problem .The heater cord is basiclly a small radiator on the inside of the cabin .On older vehicles sediment tends to fill it up so less coolant can flow through it their for less heat can transfer from the engine witch is the source of the heat into the cabin .Some vehicles also have a gate valve or ball valve that turns and shuts off the coolant flow the from the water pump witch drives the coolant every ware it needs to be in the entire system your control inside the cabin opens and closes this valve to let coolant into the heater core if you even have this valve .The best way to tell if the heater core is flowing is to warn the vehicle up to operating temp look for the 5/8 heater hoses going to the left side of the fire wall there will be 2 of them 1 is in 1 is out .One side should be much cooler with the heat on full if not its the core or the valve if you have one .

well it might be you engions not heating you see the heater draws heat from the ingion but if the thermistat is stuck open then the engion will stay cold and the heater will only blow cold air

I've had this problem. 2000 GMC uses a closed coolant system. Meaning takes and returns coolant from and to the Reserve Bottle and has little air in the engine and heater systems.
If everything appears ok but no heat. "Air Lock" is the most likely cause. (With interior heater set to full heat) Solution; 1. Make sure water pump works. 2. Drain about 1/2 engine coolant into container. 3 Remove both heater hoses from engine side and flush heater core in both directs through heater hoses with garden hose. 4. Reattach heater hoses in correct locations. 4. Refill engine with coolant. 5 Start engine and run for 2 min., use caution when topping up coolant.
6. Most 2000 GMC have twist off caps with plugs located mid way on heater hoses. with engine cold, start engine these caps may be loosened to allow trapped air to escape. Do not attempt with engine hot due to hot coolant injuries. This may take more than one attempt to remove all air from heat system. 7. Lastly most 2000 GMC water pumps have a bleeder plug,( 3/8" square driver plug) located on the water pump. With egine cold this plug should be removed to remove any air. Reinstall plug with thread sealant.
Hope this helps cheers

Yeah you probley have air in the coolent system try letting it run untill the temp is about 195 degrees and then cut it off lwt the water **** down and out mor in and do it over untill you got heat

This sounds like your automatic climate control is starting to malfunction. Check to make sure your coolant is full, and temp is not fluctuating, and when your vehicle is warmed up, try using the low setting and feel for air temp. Is it warmer than if you turn it up? When at idle the vehicle is not producing heat the same as if you are driving, putting load on your engine and more air/fuel combustion means more heat, which is why you can feel heat while driving. Ideally you should feel heat as soon as the engine is warming up, getting hotter as it reaches peak temp of 190-210 degrees. You can try to make sure your water control valve is not blocked, and all electrical connections are secure. This will be located close to your firewall and connected to the coolant tubes that run into your firewall to your heater-core. Also use recirc (setting)to try to summon as much heat as possible, however ultimately, you may need to take you vehicle in for service. If it only warms when driving defrost will be an issue. Good luck.

1suspect thermostat either primary for engine or secondary for heating system if fitted.
2 suspect that heat valve maybe jammed in the closed position so the mechanism can not open the flow to the cockpit.
3 suspect air in the system ensure the sytem is fully bled so the water can flow freely.

My 05 sentra with 79k miles heat will warm up and then get cold after a mile of driving, we have tried to get the air pocket out, the mechanic stated he thought it could be a blown head gasket, another mechanic said it was a bad heater core. Any advice would be appreciated.

Water pumps can stall out, but do you have air trapped in system.
Had you recently had the system "open" to replace hose, thermostat, temp sensor. Some Ford and GM have a bleeder screw on a high point in cooling system to bleed out trapped air.

Check your trans fluid color. Since the trans cooler is built into radiator (automatics)

IF the engine is overheating the trans CAN overheat
IF the trans is overheating the engine CAN overheat

They share the same cooling source and trans fluid gets hotter than oil, but yet it has a wimpy cooler built into radiator. Maybe add trans oil cooler to system.

Also outside temp affects the cool down rate of the radiator, ie...hot air trying to cool down hot radiator/engine is less effecting than cool air cooling hot radiator/engine