If youy lost most of the coolant you will not get heat, and the gauge will not read right... The gauge does not read air temp well.

If you lost the coolant and did not know it, you could have fried the engine.

A toasted engine can respond as you have said.. I am not saying this is what happened, but it is possible..

One day a time ago I had a near thing happen.... I lost my coolant at once from a split radiator. The coolent went out from low on the rad and so I saw nothing.

I noticed the gauge climb and then drop as it occured by chance. I could hold no water as I found at all after trying too.

So check for coolant, a belt and a properly running water pump...

As it is I think you may have more than one thing happening, but did you set coolant for being in DC where things are perhaps cold enough to freeze?

Wind chill will effect a hot radiator perhaps faster than a cold one...

Other things to seek are vacuum lines which may have come loose due to cold causes these to become bigger, and I hope you find one off some fitting on the intake some where.... Mac