05 Impala 3.4l fluctuting temperature

My 05 impala is going through wild temperature swings. For the last month, it has been floating between 180-210°. Oftentimes the temperture gauge swings 30° in a matter of a few seconds.

I had an intake leak. Replaced intake gaskets, no change to the temp swing problem.

I replaced the thermostat. No change to the temp swing.

Had a bad crank pulley (wobbly). Changed it. Made the temp swing issue even worse. Now bounces between 160-230°. Also, after the car runs for about 5 minutes - driving about 2 miles, the engine starts missing. Also, my heater is intermittent. I usually get heat as the temperaure gauge hits 140°. Then the heater starts blowing cold and comes in and out.

I bled the system for air. Coolant is not leaking and level is OK.

Any ideas?

You have a head gasket out or possibly a cracked head. When this happens it gets air in cooling system therefore the flucuating temp gauge.

Thanks Mechnark - you identified the problem correctly. The car is currently in the shop getting some new head gaskets. I do not have the luxury of a heated garage, and this is my only transportation. Kinda sucks spending $1000; but, I need a car to get to work.

My intake gastets were just replaced a couple weeks ago. Had an external coolant leak. I am going to the same shop. WOuld some of the same labor steps be required to replace head gaskets as were already done for the intake gaskets. I'm worndering to see if I can agrue a reduction in labor costs since both problems were not identified at the same time and I do not want to pay for rework.