08 boxster overheating

[Vza]

So I purchased a 2008 boxster w 42000 miles from a scrapyard. Took for its maiden voyage on the highway and the engine overheated. I added some coolant before leaving cause the low coolant light was blinking. About 40mins in the temp gauge jumped and was pinned to the right with no gradual increase. I also smelled electrical burning. Warning light blinked engine too hot. Immediately shut down...cooled off got it home. The 'eng.too hot 'came on again as I pulled in the garage. Hope I didn't do ant damage to the engine. Today it cranked right over....let in run half hr and the temp gauge didn't move. This issue is the 1st to fix on this long restoration. I'm thinking the thermostat isn't opening and probably needs to be replaced along with the temp sensor. Or...faulty temp sensor isn't allowing the thermostat to open....no signal. Any help would be great. V