We give our cats one full can/day of canned food so it's at room temperature. Occasionally we've gotten off schedule for various reasons and have had partial cans refrigerated. We haven't tried heating it so I can't speak to that. When it's cold they don't love it as much, but still eat it. (perhaps it doesn't smell as much when cold?) Just as I am fine with a cold turkey meatloaf sandwich even if it's not as good as when hot, I doubt it hurts them.
This thread reminds me of my grandfather. Back when he was alive they lived on a farm and had quite a lot of barn cats which he appreciated since they kept the rodent population down. He would feed them enough scraps so that they wouldn't starve or leave if the rodent population was low and he'd provided some very rudimentary bedding/shelter so they wouldn't freeze in the cold, but beyond that he didn't 'care' for them as one would pets. As he got older he seemed to get more concerned about what they might like. So every night after dinner he would heat up the scrap mixture before carrying it out to the barn. The cats LOVED this. Once he started making them a hot dinner every night they'd see him coming and all swarm around him excitedly until he poured the nasty mess into their trough. Knowing how sensitive cats are to smell I'm not surprised. This stuff STUNK big time.