Not sure what punctuation to use

Punctuation is not set in stone, there are differences in style and purpose.

Your first sentence is fine, instead of a hyphen you could use a comma, but it's fine as it is.

In the second sentence I would use commas in place of both the colon and the semi colon.

Colons normally imply a list of some sort, there's no list, just an ecplanation.

Semi colons are used to connect two sentences. That means that when you use a semi colon, the text each side should make sense in it's own right.

As in, "I decided to go to the pub; Stephen was sat in his usual spot."

In this example both I decided to go to the pub, and Stephen was sat in his usual spot, make sense on their own as sentences so a semi colon is appropriate.

In your example " thermos, which is Greek for heat, and regulation, which means control," does not make sense on it's own.

However, looking as your sentence again, the two clzuses either side of the colon do make sense on their own, so you could put a semi colon there in place of the colon between you and thermogenesis.

Hope that helps.