The charger box part does get fairly warm normally, was it too hot to touch?
If too hot to touch or hold then it could be a safety issue, maybe not the correct size or defective...

I just checked dh's laptop but he isn't actively using it right now, the box part is cool.
*you might compare how warm yours gets during active use vs laptop on but not using it...

I wouldn't recommend ice thing. Maybe a little rack or something to lift it up for better air circulation?
And keep papers and such away from it..
But you might mention it to the guy where you got this one, maybe try a different one to see if it does the same thing or not..