At idle, temp should be around 30C. Operating can be higher than 50C, but some CPUs fail a bit above 60C.
I would guess that attachment of heat sink is suspect. Take it apart and inspect for issues (like a cracked mounting frame if plastic, or a slipped mounting pin). Everything should fit together with only slight pressure - especially any Skylake builds.
Needs fresh application of thermal paste when you re-assemble.
As to thermal paste - pea method is probably best - Youtube has good videos on this.