That's a bit high for idle temps and about as high as you'd want to see it go under full stress testing, even with the stock Intel cooler (which is fine for a non-overclocked processor but you'd want something better for overclocking).
If you are using the stock Intel HSF check to verify that everything is copacetic with the installation and that all the push-pins are fully seated. However, if you have to fiddle with it at all you'll want to pull it off and clean off the thermal compound properly and re-install it, properly, with completely fresh thermal compound.
...and if you're going to do that you may as well spend ~$30 on a decent HSF, such as a Xigmatek S-1283
Yeah, this is a tall recommendation without knowing the particulars of your scenario but your issue is rather common amongst the forum and the prescription is typically the same.
HTH, cheers.
Brad