To warm up or not to warm up, and...?

In my mind, equipment doesn't need to warm up so much as reach stability.  Worst case is you make this take a little longer, while trading longer equipment life.

As others have said, heat is the enemy of a lot of components, especially capacitors.

If you are using a component in any sort of enclosure, I would recommend lots of cooling, as well as making sure that you don't just recirculate hot air inside it.

If your gear lives in an open rack, the most I'd suggest is maybe adding tall feet to elevate the component to ensure it gets fed plenty of cool air.

In my experience most receivers don't get hot to the point of needing cooling but if you have it in a very enclosed environment yes cooling might be needed. If you would've listed your receiver model (big fat really doesn't provide much info) and maybe how is it positioned and installed we could provide some more data. Assuming a regular home environment I would say cooling is not needed and the receiver would be best without it.
The only piece of equipment ever I had need to cool is a 6C33C-B amp basically to extend the caps life.

IMO from what I have read it is not so much the heat that will degrade the unit as much as the heating cooling cycle. This is why most high end manufacturers recommend you keep your equipment on all the time. They use components that are designed to handle high temperatures. Where those components start to fail is when they are put through constant heating cooling cycles (on off on off). This will cause expansion and contraction that will lead to failure. Example I run my old Sansui 70/70 in my wife’s business it has not been turned off for 28 years except for blowing out dust and is still running strong. I do not see an issue with your situation as you are still maintaining constant temperatures. As for the sound trust your ears and don’t over think.

i hear better sound quality when my amplification gear - tube or ss - warms up, usually from 10 to 30 min in

we are talking about hegel, van alstine, odyssey, ayre ss gear, as well as cj, arc, pl, air tight tube gear

that been said, i am careful to keep hot running tube amps cool and air circulating... use quiet fans to move the air past the power tubes e.g. 8x kt88 kt120 etc etc... i am pretty convinced  (as is ARC) that letting these high power tubes run cooler makes them last longer

For those who don't understand, the winking smiley face means it's a joke, not serious.