After having had a couple of complete runs of the game, you should be able to do this relatively easily. Just be quick, because the longer you take through the game, the more heat drinks you'll need to use.
Avoid things that take unnecessary time, like picking up items you won't use. And kill enemies quickly with guns. And make sure to not use more than three heat drinks! (You can use three, but not four!)
One of the easier achievements to unlock in this game. There really isn't much more to this.
You'll probably also get "Quick Before You Freeze" at the same time, if you haven't already.