Yes, 86 is high. 90 is where the CPU starts throttling itself to make sure it doesn't get damaged.
70 for a GPU is no reason for alarm.
Laptop coolers are useful, the air in for your laptop is below the laptop. w/o cooler you have 5mm of air there, and it is heated by your underplate.
With cooler there's a lot more air, and a fan pulling it from further away. Temperatur of the air supplied by the laptop cooler should be lower than that supplied by just the laptop. And that allows for better cooling.
Considering the minimum CPU requirements and you not having issues with BF1, which came out 3 years later and should be harder to run, there should be a driver issue somewhere.
Easiest is to get the Nvidia automatic driver update thingy which is called . . . . experience?
If the latest isn't great you should start scouring the warface forums for mention of the 1050, the Acer VX15 or your specific i5. Considering the temps, start with the i5. Then see if there's a driver/setting/something which makes that particular piece of tech crash with that particular game.