Just to compile and summarize for the OP and others with significantly higher than "standard" temperature tap water:
Keeping processing temperatures close throughout the entire process is more important than developing at 20°C/68°F. The danger is thermal shock to the emulsion which can cause reticulation (and does! don't ask me how I know...). Try to stay within +/- 2°C at least.
Developing at higher temperatures requires a shorter developing time. There are tables published to determine the correct time at higher temps. If developing times are too short, use a higher dilution or different developer (make sure you have enough developer stock for the amount of film you are developing though). Other steps are not so temperature-sensitive.
If your emulsion becomes too soft at higher temperatures and regularly suffers damage, search for formulas for tropical developing (easy to find with Google). 85°F is quite high, and may not be good for some softer-emulsion films. I would imagine that Kodak and Ilford products would hold up well.