Usually these coolers are very good, and the CPU runs fairly cool anyway, not needing an even heavier cooler.
What about ambient temps, and your case cooling?
Exhaust fans at rear and/or top are important; any fans blowing
in to your case are less so.
The OEM compound on the stock cooler actually works well, but it's a one-shot deal. If the cooler is ever taken off, or even moved (breaking the seal to CPU), it must all be disassembled and cleaned up.
Then reassemble with something good like Arctic Silver rubbed-in well on both parts, and then mated.
Sometimes the 4 Intel mounting holes for the cooler on the motherboard will loosen up a bit, if you mount/unmount the cooler a coupla times. This is a good thing.
Yeah, you'd better take it all apart and get to 'know' the cooler installation very intimately...
Once you get it all assembled really slick, often only then will you realize it was in fact improperly configured before.
Your temps don't sound too-too bad (a bit high perhaps).
Often this is just poor case ventilation + hot room + overclocking etc.
Let us know what happens, good luck.
Regards