sudden extreme rough idle, no codes but several recent issues

I’ve suddenly had issues with my car, a 97 Maxima, over the last week. No issues at all before these events.

First, last thursday a coil went bad which produced #2 cylinder misfire and ignition circuit codes. I replaced that coil and it solved the problem.

Then yesterday, the car starts overheating on the highway on the way home from work. It ran normal temperature that morning. This was not severe and I could keep the temp on the gauge at the normal level by running the heater. I never let it get close to H.

Then today:

I drive the car again to work and it actually stays cooler, being just a hair above normal but nowhere near H. It ran normally until I got off the highway near home and suddenly idles terribly, shaking the whole car. It also shook some when cruising but did not lack power. Really felt similar to the misfire caused by the bad coil last week.

I baby it home and the whole way get no dash lights or warning of any kind. The car never overheated. Everything I can see checks out –

• no strange noises
• no leaks
• no smoke, from tailpipe or otherwise
• no burning smell
• full oil
• full coolant
• no sign of water in oil vice-versa
• radiator fans running
• no CEL or other warnings

Both radiator hoses are hot but not abnormally hot. Nothing at all wrong that I can see.

And the strangest thing is despite seemingly idling on two cylinders, there are no codes set. The idle speed is normal but just extremely rough.

Do you think the bad coil, overheating, and now rough idle are related? Where do you think I should start here?