Yeah, I try to use the word, "notebook" because they should never be used on a lap (or bed or carpet), at least not without sitting on a hard, flat surface.
It makes sense your performance is better on the charger. Unless you changed them, typically the Power Options are set to increase battery runtime when not plugged in. And it does this be slowing everything down, which also decreases performance. Typically, the screen's brightness dims a little on battery too. And since performance increases when plugged in, so does heat generation.
As far as a cooling pad, look at the cooling vents on the bottom of your la... err... notebook. Then look for a cooling pad that has fan vents in the same place as those vents. Also, look for a cooling pad that comes with its own power supply. No need to place additional demands on the notebook if already heating up. If no power supply (and most don't these days), then get a
USB Wall Adapter to power the pad whenever possible, instead of using one of the notebook's USB ports.
Are you saying this is a new notebook? If so, is it still under warranty? I would worry about the smell too. It is not uncommon for new electronics to give off "
that" smell. But that should fade away as you use it. If this notebook is already several months old, or older, it should not be producing a burning smell any longer. If still under warranty, I would give them a call. If it is coming from the battery, you sure do not want it swelling up and cracking, for example - or worse, catching fire - or worse, exploding then setting the house on fire!
If no longer under warranty and the smell persists, I would consider taking it to a professional repair shop and ask them to check it out.
When plugged in, does the charger get "very" hot - as in almost too hot to touch?