Aiyo spend so much money for the lappie's couple degrees cooler. Your laptop have been designed to take much higher temperature and it have been designed to vent out the much needed heat from the laptop effectively with the builtin fans.

With these laptop cooler , it is only cooling the physical outside of the laptop and help dissipate the heat that is produced by the faster Notebook HD

My thinkpad is also much hotter at the bottom but so far 3 years using it without any elevation or fan seems to be no problem.
But what do i do is that I used 2 eraser . rubber to stick at the bottom behind of my laptop to elevate it to 45 degrees and this help make my laptop more ergonomic for typing as well as helping it to dissipate the head away from the laptop
It helps a lot and it ;s portable.

The heat that you feel coming out from laptop keyboard is always there regardless how cool your laptop cooler is because there is a heatsink existed below your keyboard to help dissipate the head from the laptop thru the gaps of your laptop

Dont believe, take apart your laptop . Any desktop engineer can tell u that.