The dog days of summer

This is a picture of my laptop at work when earlier today it suddenly and silently cut to grey.The two areas on either side looking sort of like shark gills were feeling a lot hotter than electronic equipment usually likes to be, and the underside of the laptop, sitting flat on my desk, was just as bad. So I'm guessing that the problem today, and the intermittent problems I have been having (occasionally when connecting to the office remotely, which I really find inconvenient) could be heat related.

Why don't they make big smokestacks for laptops to carry the heat away and put it as far away from the unit as possible? Or put radiators under the keyboard (which has lots of open space) instead of in a thin strip to the side? That way my fingers would be right where they need to be to know that the unit is feeling a little feverish and I should try to slow things down for a bit.

I have the back feet of the laptop propped up slightly to improve the air circulation somewhat, and those vents feel twenty or thirty degrees Celsius cooler presently. Let's see whether this helps, since I think a replacement is not going to be in the cards for now.