I so understand - I live in Houston where it is hot and humid.  I walk in the early mornings.  I hate getting out of bed early but once I am walking, I am ok.  You might want to think about a treadmill - go to a resale shop or check craigslist.com to find one cheap.  Sorry this isn't the magic answer you were probably looking for.

What about Mall walking?  Especially in the morning or later in the evening when they aren't busy.  Or you could find a nice tall office building and climb the stairwells.