MacOS – this button on the MacBook Pro Touch Bar

There is no way to customize it yet. Seems to be ample space to place them around the "Play" icon.

The normal operating temperature range for silicon is much higher than is comfortable to the touch. The heatsinks & fans are directly below the top of the keyboard along the hinge opening. I too have found the upper edge of my MBP to be uncomfortable to touch -- typically when I'm debugging using the F() keys.

My recommendation would be to use a product that allows you to manually adjust the fan speed in order to run the fan at a higher-than-minimally-necessary speed to lower the temperatures accordingly.

I personally use iStat Menus. In that tool, under 'sensors' is a button to 'Edit Fan Rules'.

Incorporating feedback from the OP to create a more comprehensive answer:

Alternatively, if you believe you may have a hardware issue, a trip to the Apple store might be warranted. The OP had a hardware issue that, while mitigated by the iStatMenus approach, really required a hardware solution, including multiple trips to the Apple store, to ultimately resolve.