To emphasize this point, go outside at noon in the summer and mark off a square meter on the sidewalk. That square of concrete is receiving about 1000w from the sun.

Now imagine a magnifying glass that big (or more practically a fresnel lens) concentrating all that light into one square inch. That's a lot of power. When copper connections don't work perfectly they have nonzero resistance, and the current running through them turns into heat by I^2R.