I don't think there are any direct routes, so here's what I would do:
1. Catch the tube from Heathrow to Holborn on the Picadilly (blue) line
2. Go from Holborn to Liverpool St station on the Central (red) line (4th stop)
3. Catch the Stanstead express (every 15 minutes) from Liverpool St Station to Stanstead Airport
I would allow an hour to get from Heathrow to Liverpool St Station, and an hour for the Stanstead express. 3 hours to be safe.
You can get a tube map here:
There's a travel timetable option for the Stanstead express here:
http://www.stanstedairport.com/assets/Internet/Stansted/Stansted%20downloads/Static%20files/PAXTravel%20Options_Jun09_onA4.pdf almost 9 years ago