'98 Taurus running hot and burning oil

This car has had radiator issues since I bought it two years ago. The heater wouldn’t work, just blow cold air. So I flushed everything out and it was runnging fine up until this week. It has rust in the overflow, and overheats if I use the AC.



The other day, it was running a bit hot as I got to work. As I was backing into a parking spot, the oil light came on. I checked the oil and it was about two qts low. So I refill it and again yesterday it does the same thing.



With it running a bit hot, will that cause it to burn oil? It’s not smoking and there are no leaks. Never had a problem with the oil before.



Thanks.

It seems you just want to keep this car going without putting much money into it. The running hot condition is ongoing and you have probably got the oil thinned out to a point it is too thin for the oil pump to build and keep the oil pressure high enough. When the oil thins out in the heat it burns off quicker too.

Easiest option is run a heavier weight oil, perhaps 20W-50 or straight 30. If you live where winters get cold you can go back to 10W-30 for the cold weather months. Either do an oil change and refill with heavier weight oil, or start adding straight 30W oil to what is in the motor now.