Postscript:
A number of readers responded to this article with some interesting comments.
First, many people believed that Fahrenheit originally set 100 degrees to be the temperature of the human body. In fact, according to several sources I encountered, it seems he did use body temperature as one of the upper defining points of the thermometer. But, oddly, he chose 96 and not 100 as the number representing that temperature. The reasoning, it appears, was that the coldest salt water could go before freezing was 0; the coldest pure water could go before freezing was 32; so body temperature should be 96 (which happens to be 3 x 32). He later adjusted his scale when he discovered that the body's temperature was more accurately 98.6 degrees. He ultimately gave up on this measure, instead calibrating all thermometers by using freezing water and boiling water.
I could find no explanation for why he chose 32 to be his magic number, rather than 30, 25 or 100.
And finally, just when you thought that Celsius really did make more sense, one ready pointed me to an interesting website on the history of the Celsius scale. According to Anders Celsius's original notes, it seems he originally set zero to be the temperature of boiling water and 100 to be the temperature of freezing water. So rather than going up as it got hotter, the Celsius scale went down!