I got the one that leads to Whiteout Valley, but that didn't help. Because I saw in Mariowiki that I needed a "heat-based" sticker, but it also said that you could only get heat stickers after Snow Rise. How can I get a heat sticker such as radiator, hair dryer or oven?
The radiator thing is obtained in World 3-10: Stump Glade. After completing the first three games and you are dropped to the star room, the host Snifit will offer you a chance to clear a special stage. Snifit up and accept the challenge by agreeing (in a legally binding way) to the fact that the host can not technically guarantee you'll live.
The special stage involves answering three questions correctly again, but this time you have to score five hits in Snifit whack-a-mole before you can answer each question. Completing this final stage drops you into a room with the "Awesome Thing"! a radiator!