I don't know if the chip can go to that temperature and it's good for it (I doubt it) but speaking only from a material point of view, the spread between both temperatures is far too large and it will cause a lot of expansion in the materials when they heat up, and a lot of retraction when they cool down, and all the time. That causes a lot of stress on materials and they may break.
Now of course maybe chips are designed to face this and it's all right.
But I ran your test on my computer and I have about the same idle temperatures as you but under stress it only went 10C higher max. My CPU isn't overclocked but it's got the stock Intel cooler and the case is Antec 900.
If you're worried, I'd look for a case first because that may help a lot more than a new cooler if currently you don't have lots of air flow possible like the Antec 900, as it's a similar investment in price for high quality parts but you may see a bigger difference with the case.
Do note that the Antec 900 can be comparable to an Xbox on max fan speed if you've got one
EDIT: Wait, when I got the idle temperatures fans were on low but now they're on high and I've gone to around 30C on Idle.
