100% you should never run a computer without a cooler on the CPU. Even with a cooler CPUs can easily get over 60 degrees Celsius very quickly. Without a cooler it's probably reaching unsafe temperatures (90+ degrees Celsius) almost immediately because it has nothing to dissipate the heat.
Please, leave it turned off until you get the cooler on there so you don't damage your CPU. ๐ญ
Yeah. What else would I do after work?