Overheating car did I blow my engine

I drive a VW Jetta 2003 2.0l wagon auto. I have been having problems with my jetta. My Temperature gauge turns on in the morning when I start the car. The gauge does not show engine overheat. Ten minutes after the car runs - I restart the car and the temp light does not turn on. I took necessary steps to troubleshoot- both cooling fans work but no overheating. Today I drove the car to work it started to overheat to 260F. I stopped about every 4 min to let it cool down the trip was about 16min. to work. During this drive the check engine the light turned on. The outside temperature outside was -10F with a good -20F windshield if the weather makes a difference. My thermostat is stuck and I know that I have to replace it. My question is: DID I BLOW MY ENGINE BY DRIVING THE CAR AT 4MIN INTERVALS?

Not likely. If you had done damage you would have heard rapping or knocking noises. And the -10 degree weather halped.

Now get that T-stat changed before you DO damage the engine!

Ever considered popping the radiator cap and checking the coolant level?
Since you’ve had some chronic overheating issues and motored on, I would advise checking the oil level frequently.
Often what happens with an overheated engine is that the piston rings will either seize in the piston ring lands (grooves) or the rings may lose their spring tension. This leads to excessive oil consumption.

Did it seem like the engine was suddenly “holding back”; then just as suddenly regaining its power? If not, you may have dodged a bullet. The boiling point of a 50-50 coolant mix is 267 degrees F @ 15 PSI, so if you have a good 15 PSI or higher pressure cap I believe you’re in the clear. Souds like you live where it’s real cold so I bet you do have that 50-50 mix or better. Have Autozone or a similar place read your codes and write down the entire code, especially the ones that start with “P”. Post them here and people will give you the scoop.