60 degrees over ambient? Ha - maybe towing a pop-up on flat ground...
Our 2002 Burb has an instrument panel gauge for transmission temperature, but I use a scangauge which is considerably more responsive and accurate. On an 85°F day and towing our 8500-9000 pound TT on flat ground at average highway speeds, we'll see transmission fluid temps of about 160°F. On a long hard climb it's not uncommon to see the tranny temp get up to 220°F for short periods. Since that's about as high as I want to see it, it's extremely helpful to see just how long it's up there and how quickly it comes back down.
I'm afraid the built-in instrument panel gauge doesn't show the true temperature until damage would already have been done. I'd recommend something like the ScanGauge for anyone who's really serious about protecting their transmission.