Did space suits solve it? Astronauts are in a vacuum, so heat transfer can't take place except through radiation. Meanwhile the cold air at the top of the Himalayas is very good at pulling the heat out of you.
The "space is cold" thing is actually a pretty good shibboleth for people who don't know that much about engineering things in space. Most space systems have to put in effort to reject excess heat than to hold onto basic amounts, hence those giant radiators and the high emissivity paint that gets used on most things.
But mechanical parts of the space station can be as hot as 120C (250F) and as cold as -150C (-250F), so I'm pretty sure you do want thermal insulation :-)