Do you need cooling pad for long-duration hard-core computations on MBP M1?

You do not need a cooling pad.

There is something wrong if your computer does not cool adequately.

Keep your Mac notebook within acceptable operating temperatures - Apple Support

Should I get a cooling pad if the temperatures are constantly above 100C?

If the temps get that high, the computer should clock back or shut down. As the others point out, if your are seeing temps that high, something is dreadfully wrong with either your hardware, software, or usage patterns. A chill pad would be like putting a duct tape on a deep stab wound.

Also, chill pads are relatively ineffective on Unibody Mac notebooks like the M1. Prior to the Unibody design, heat-critical components touched the case bottom which became part of the hear dissipation system. Chill pads worked great on those. With the Unibody design, the logic board is "hung" off the upper desk and the case bottom does not contact components. Chill pads are not very effective with that configuration.

We can see if you have a software issue that is causing the excess heat if you post an configuration snapshot. Fortunately there is a safe, secure way to do that. 

We can quickly and within the confines of these forums help you determine what issues are at play if you use EtreCheck Pro, available here:

https://etrecheck.com/index

The free version will do nicely for this purpose, although the app is worthy of our financial support.

We can see hard data about drive performance, software issues, and RAM usage. Etrecheck is the development of a long-serving and trusted contributor here expressly for displaying information in these forums to help us help you. It will not reveal any personal or secure information.

Run it, select “Report" from the left-hand pane (scroll down to the bottom of that pane to find):

When its report displays, click the "Share Report" icon from EtreCheck’s toolbar and then "Copy report” from the resulting dropdown.

⚠️ Please DO NOT highlight the text in the report before using Etrecheck’s “Copy report” command—that will garble the formatting and make the report slower and harder to evaluate.

NOTE: Changes in late 2018 to the forum software require you use the “Additional Text" icon (see example below) to embed the report into a post:

Paste the report into the resulting “Additional Text” window:

Hi,

M1 usually should not be running that hot. Especially compared to Intel processors, M1 usually runs cooler and fast too. Since you have the MacBook pro, it has a fan so it should be fine. If you feel it is running uncomfortably hot, a cooling pad might help but not all of them make a difference so do your research before buying a cooling pad. Regardless it should not be uncomfortably hot so it could be an issue with your computer.