Like /u/denmax94 said, those thermal pads aren't for convective heat transfer (like a fan over a heat sink), but are for assisting in conductive heat transfer (movement of heat between two bodies in contact).

The Peltier coolers you linked work in the same way, but they use electricity to move the heat from one side to the other, but those are also made for conductance and would need a heat sink on the other side.

The hard part is fitting something sensible between the keyboard and your desk. The only real method I can think of is using a set of little heat sinks like this attached to the bottom with a laptop fan blowing on them. I don't know how well that would work, but it may be small enough to fit entirely under the keyboard. I get it, I'm a sucker for cool keyboards too.

I used these: https://www.amazon.com/gp/product/B07YWLTZPS/

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And these smaller ones to "fill in gaps" https://www.amazon.com/gp/product/B078KB7V5J/