I'm posting a guide mostly to highlight 2 important bugs: One positive, one negative.
The negative: You should do this scenario in one sitting. If you quit and reload, your day count will go down by 1. This can keep happening - when I was testing this out, I got my day count down to negative 5.
The positive: You only need to hit a positive 10 day count - not the 20 that the instructions say.
As for how to do it, I don't have a thorough guide. A lot comes down to RNG. My general strategy was: Keep the frozen counter as close to 8 as possible. Keep a balanced but tight deck - mostly resources, very few idea cards, upgraded resources where possible (the "dried food" 2x food card, etc). Some of the upgraded people are good too - especially the shaman (gives you the option to increase the frozen counter by 1, by sacrificing a food).
Let monsters hit you, but don't waste turns to let them hit you extra. You'll get hit enough as-is.
When your life is down to 1, you want to grab a zero-temperature turn or two. First finish the region you're in so you can travel whenever you want, and you don't care about card draws. Then use the special power to increase health at the cost of temperature, and bring yourself back up to max health. You probably need to kill 2 cards also in order to get your temperature down to the minimum. Then I'd let 1 or 2 turns go by, burning frozen counter in order to increase the zero-temperature-days counter (the win condition counter)
You could risk doing more than 2 turns, but the first time I tried that, I then got an unlucky streak and lost. Better to do a slow and steady approach.
Also any time you're ready to travel, burn any fatigue/terror/unnecessary cards that you want.
As a general strategy, use tokens to keep track of how many of each resource you have. That's good in any scenario, but in this one, you may be forced to burn "good" cards to get your temperature down, or because you want to kill a terror/fatigue card but also need to kill a 2nd card to do it. If you keep track with tokens, you'll know what you have extra of, and what you don't have enough of. I used poker chips.
Good luck. Fun game, but quite a few bugs.