I live in California, so heat and sweating are commonplace most of the year. In the summer the average temperature range is 85-100F (~30-38C). I've found that binders over years of wearing tend to hold on to a little bit of smell, but if you take care of them, it should only be noticeable after washing if you're smelling close enough for your nose to touch.
You're not supposed to dry them in the dryer, only line or flat dry, but if you don't do it too often, you can get away with it. It'll shrink the binder a little bit, which can be good or bad, but the dryer sheet might help to get the smell out.
My advice would be to wash it in a washing machine, on handwash/delicate/gentle cycle. Make sure it's cold water, and use a generous amount of laundry detergent (I've found liquid works better than powder, but whatever you have). Once it's done, hang it on a hanger and put it out somewhere to dry. Outside (but out of the sun) would be the best choice since you said your apartment's no good, but maybe near a window would work as well. (I just hang mine in my closet and it dries in an hour or two, but it seems like that wouldn't work for you.) That's always how I wash mine, and they've held up just fine after 3+ years.
If that still doesn't get the smell out, spray the thing with vinegar or febreeze (you can soak it too if it's really that bad, but I would try spraying first), let it sit for a little while, then wash it in the machine again. That should probably do the trick. Good luck!
