Camaro heating problems

My 95 Z-28 started showing a high temp while stopping at a red light. On take off, the temp would go back down to normal within 2 seconds.
Or, If I put the car in neutral and gave gas, the temp would go down. This was happening off and on. No rough engine, no smoke, no antifreeze smell, the only symptom I had was the temp gage. The antifreeze looks dirty. My car is at a chevrolet dealership, that i honestly do not trust, but it was near me. The answer they have, with a block check, is the exhaust is leaking back into the cooling system. No thermostat check, no oil check, no pressure test. Im not getting any answers but, replace the engine. They dont know for sure if this is the problem. When i mentioned a gascket may be cracked, the answer was, not got that far into this yet. No plans to check anything else, they want me to replace the engine. He told me if he replaced the gaskets, it was not a good idea, because, I didnt know how long the car would last anyway. Okay, so instead, put an engine in it, that is used, and after 91 days if that goes bad, im out $8000.00! Im taking my car to a dealer I trust to have this checked out. No evidence of coolant on the engine. And like I said, no problems running or idling, just the temp gage, and the heater will only blow cold air. The car doesnt run as if its hot, or, smell like its hot, and the temp goes down way to fast for it to actually be hot. Nothing else is wrong with this car, so replacing head gaskets if you have determined this is the problem would be great. When I asked if they had seen any anntifreeze leaks, the answer was, " your antifreeze is dirty". Could this be a heater core problem? Or, more of a head gascket or block problem? All info is appreciated, greatly.

Get your car out of there, pronto.

You've already said yourself how it needs to be checked out, take it somewhere else. When the radiator cap is off and the motor is running, do you see any bubbles coming up (thermastat needs to be open fo rthis, BTW.)

I would drain, flush, and bleed the system.

I just went through the exact same thing with my 97 Z. I had no heat just cold air and the temp gage would get really hot when stopped or idling but, dropped back to normal very quickly when moving.

I had a massively clogged heater core, I had it replaced. The problem went away for about 2 weeks. I think my problem is that I did not have the money for a flush, just a drain and fill on the coolant. Have them look at the heater core and do a full flush! I am going to get mine looked at again shortly when I get paid. I think I may have clogged the heater core again and hopefully I can just flush it.

Not sure if you got this fixed yet. .. but there's probably a good reason you dont trust that service shop. Umm... THEY ARE IDIOTS! ...and/or just trying to get your money.

This is not a thousand-dollar problem. This is indicative of a cooling system that hasn't been bled (big air bubble around temp sensor which registers very high temp when coolant doesn't flow). Or likely related to your heater core issue. It should be blowing hot air. Bypass the heater core with a hose and see if the temp spike goes away.

Take your car home NOW!
Once there and cooled off, remove the heater hoses going to the heater core. Get a 5/8" brass barb splice (avialable at Home Depot) and put a couple hose clamps on it.
Next. Drain your coolant. Take hoses off (lower radiator, heater at radiator) and let them drain. Next get 2 bottles of radiator/cooling system flush. Hook your hoses back up except for the 2 going to the heater core. Now, fill the radiator with water and add one bottle of flush along with it. Start the engine and let it idle for 15 minutes to half an hour (if it doesn't over heat) make sure the fans come on. Then let it sit over night (IF it won't freeze) and then drain the system again. Do this again with the other bottle of flush. Next, fill the radiator with just water, run the engine for 15 minutes to get up to operating temp and circulate water. Let it cool, Drain the system and have a look in the radiator. If the radiator is full of scale and crap, fill it with vinegar & water mix (75% vinegar 25% water). Let it sit 48 hours then drain. Replace the thermostat with an all brass high flow type (auto parts store). Replace the heater core (it is probably plugged and if you flush it it'll probably leak. Hook the hoses you had the splice in up to the heater core and refill the system with 50/50 water & antifreeze.
This will net you a VERY clean cooling system for VERY little money.