Laptops do tend to run a bit hot, just because they cram so much stuff into such a tiny space. Some brands of laptops just run hotter than others though. I have no idea if your model of laptop is one of those that tends to run a bit hotter than the average or not.
If it is consistently going above 60 deg C and staying there, that would have me concerned. A short peak at 60 deg C isn’t uncommon in laptops, and if it was just a short peak during heavy use that wouldn’t bother me too much. Hovering around 70 and peaking in the 80s is definitely too hot.
If you have a fan monitor, make sure the CPU fan is spinning.
It also might be a good idea to get a can of compressed air to blow the dust out of the inside of the laptop. Most laptops have vent holes somewhere close to the CPU.
Usually there is a setting in the BIOS for the thermal shutdown temperature. Exactly what this should be set to depends on the specific CPU you have installed. Most mobile Intel processors have a max temperature of 100 deg C. Note that this is the temperature at which the CPU will cook itself to death fairly quickly. For long term reliability, you are going to want to keep it a lot cooler than that. I’d probably set the BIOS shutdown temp at somewhere around 80 to 90 deg C.