definatley isnt good
most consumer electronics will be rated for an external ambient maximum temperature of +40 degrees celcius or so
if your xbox is pulling 60 internally at room temperature (of say 25 degrees) then it's going to break sooner or later.
I cant remember where the temperature probe is exactly in the xbox, i suspect its measuring one IC or another
a good rule of thumb is that if you cant hold your thumb on a component that has no heatsinking for more than a few seconds, its waay too hot and it will need cooling. and if you cant hold your thumb on a device with a heatsink for more than a few seconds, put a bigger heatsink on it or cool it another way
to cool my box a little i've cut out the jewel and bunged some mesh in, i'm really too lazy to put a bigger fan or mod it much more right now, but i'm getting temps of around 48 running games, and thats a 1.1 xbox
seriously i'd look at some extra cooling, read the tutorials.... the 80mm fan is a good compromise if you like a quiet xbox. an 80mm 12V fan is better, a bit noisier but cooler!
your xbox wont fail overnight so dont panic, at 60 degrees though, i wouldnt expect it to last for the warranty period!
....they test component lifetime by running them in artificially high temperatures for a time - say, if its specced to 40 degrees, and 5 years they may run it at 100 degrees, it fails in a month then some mathematical relationship would give a expected lifetime at 20 degrees, maybe 1 week at 100 is equivalent to 2 years at 20 or something like that,
not entirely accurate, but gives you an idea