Does a vertical stand for the console help with cooling

The console is designed with adequate cooling. External cooling solutions can actually compromise this system by changing static pressures as well as present risk to your console shpuld they be plugged into it, and can void your warranty since they are unlicensed peripherals.

Regarding this, you will need to read what's mentioned here => How to position and ventilate your Xbox console | Xbox Support.

Here is a little guide. Also, get some compressed air on the back and sides. Maybe is dust. Here is the proper
use of the vertical stand.

Make sure you use only the stand designed for your Xbox, which helps console stability and operation. Without the stand, vertical positioning blocks a cooling vent. If you don't have a proper stand, put the Xbox as the guide says.

EDIT: If nothing helps you must repair it as others have said.

I would not recommend that you use any 3rd party cooling on the consoles.

Also using a vertical stand is perfectly fine.

The One X and the One S can stand vertically. The original Xbox One does not have that option.

For more information, please visit: https://support.xbox.com/en-US/xbox-one/console/using-the-vertical-stand-for-xbox-one-console