Safe temperatures on i5 6500

[danielrc14]

Hi, I have a i5 6500, and I have the following core tempratures:

• 
  ■ Idle: 35 °C
  ■ Playing DOOM: 42 °C on average, and 47 °C maximum
  ■ Running a blend test with prime95: 70 °C

Are these temperatures ok? I'm asking because I had an accident while building, my cpu stock cooler came out while I was connecting some cables. I just put it on the motherboard again and made sure it wouldn't happen again, but now I'm worried if maybe there were some bubbles in the thermal paste or stuff like that, that could affect temperatures. Should I remove the cooler, clean the paste, and put it on again? Or maybe change the stock cooler, I don't know.

Thanks in advance.

 

[Ecky]

They're fine, throttle temperature is 100c.