99 grand am randomly overheating

Ahh, a typical day in the life of my room mate’s 1999 Grand Am. 3.4 V6 engine 4 speed auto trans.
Will it overheat today? As long as she drives it through town and NOT on the highway, it should be fine on the way to work (12 miles). Especially after a minor coolant replenishment (NOT with dex-kill) and bleeding at the bleeder valve.

Warm it up first thing in the morning, the heat works OK but at some early point in the trip, the heater quits blowing warm air, the temp gauge climbs to 200, but then all the sudden the heat comes back and the temp gauge drops to 150’ish, then everything is fine the rest of the trip.

Cooling system has no apparent external leaks. Her side of the garage is dry as a nun’s ____

She is wanting to ditch the car, she had many cooling system problems with her 97 grand am with a 2.4 liter inline 4. She is phobic about cooling system problems (in the same way i worry about transmissions).
Report after report point to “lower intake failures” on GM forums, car complaints site etc. She is not wanting to even mess with it, though I AM capable of replacing lower intakes on this engine (No overhead cams or timing belt to deal with)

Would replacing the intake gaskets even be worth it or is the cooling system problem just going to be an ongoing problem with or without?
She wants to sell the car but I try to tell her that a different used car will just be a different set of headaches.At least this one has a perfect transmission.

What would YOU do?