Possibly, depending on how dramatic the shift in temperature is, and for how long. A hot steamy bathroom may raise the ambient temperature in the room into the mid-90's (think sauna/steam bath), especially if you have girls/women in the house. Mine both like to take half hour showers. Now, time is another variable as it will take time for the hot steam to raise the temperature of the beer.
What I would do is invest in a swamp cooler. It's basically a big bucket that you can put your fermenter into. You put your fermenter of wort/beer into the swamp cooler, then fill it with water (or ice, or water and ice, or water and floating ice packets) to help regulate the beer's temperature. It takes longer for the big tub of cool water to shift temperature which stabilizes your beer's temperature within it.
Freeze a few bottles of water in your freezer, and add them to the swamp cooler to keep ambient temperatures down.
Beer so good, it's frightening
2013: Wamphyri Belgian Dark Strong, Trinidad Scorpion IPA, Shadowman Stout, Bermuda Triangle Barleywine, Bloody Mary RyePA, Pruno.