Date: 2/10/2008 6:44 pm EDT
3/4" particle board should be OK - do you know the joist spacing?
Regarding in-floor heat, as long as the temperature stays under 110F, the polymer backing will not be damaged (technically, you could expose the plastic to much higher temps, but those temps would be uncomfortable to your feet). Most radiant in-floor heat systems are designed to have a maximum temp of less than 100F. Check with your builder/manufacturer for their spec.
If you didn't already have a radiant heat system, I would have recomended QuietWarmth as an excellent and easy-to-install choice that has been tested to be compatible with Avaire.
I have both QuietWarmth and Avaire in my bathroom - a great combination for cold Nebraska winter nights!