If you use the stock cooler, then there is no issue, no. They are pretty bad, just good enough to keep the CPU running. If you want better temps, you will have to get an aftermarket cooler. Even cheap ones for 20-30 will do a much better job than the stock cooler. Btw, optimal peak temp in stress tests is somewhere between 80-85°C for most people, and the maximum your CPU is allowed to get to according to specs is 100°C. So you aren't far off from optimum and a decent way off from it getting too hot. If you want to improve temps without a new cooler, you could take a look at undervolting. If your mainboard won't let you do that, Intel XTU is a great alternative. Also for realtime experimenting with it.
Also, the thermalpaste is pretty irrelevant, btw. They show little difference between the different brands.