I see a lot of bad/wrong info in this thread about draw testing, so I will attempt to clarify it into one nice post.
1. Plug the red lead on the DVOM into the 10A plug on the dvom. This is a fused circuit.
2. Set the DVOM's range to the 10 A DC range. Lots of lower end meters can't check DC amps but will do AC amps.
3. disconnect the negative battery cable.
4. Install a jumper wire between the negative battery cable and the negative battery post.
5. Make sure all doors, lights, radio and other electrical accessories are turned off.
6. Wait 10-15 minutes to insure that all computers are sleeping. (when the ecm and abs modules get power they usually have a slightly higher draw for the first few minutes as they self test ect.)
7. Hook the DVOM's red lead (should be in the 10 A port on the dvom) to the negative battery cable.
8. Hook the DVOM's Black lead to the negative terminal on the battery.
9. Disconnect the jumper wire.
10. Check the amp reading on the DVOM. This should be under .035 amps.
11. If this reading is over .035 amps, start pulling fuses 1 at a time from the fuse block under the hood.
12. If you don't find a circuit under the hood that is causing your draw, reinstall the jumper wire.
13. Open the door and gain access to the interior fuse panel.
14. Disable the interior lights, make sure that the keys aren't in the ignition, and that the door dinger isn't going off.
15. Disconnect the jumper wire.
16. Pull fuses 1 by 1 from the interior fuse panel.
17. If you find a fuse that drops the draw below .035 amps, consult the wiring diagrams for that circuit. Certian things (like ECM's, ABS computers and radios) will alway have a draw due to their memory functions, so make sure that the circuit you find with a draw is not one that is supposed to be powered with the key off. Low current draws are usually caused by shorts to ground on the ground side of a circuit or faulty components. Typically a power wire shorting to ground will cause a the fuse for that circuit to blow.
18. Repair any Faulty components or shorts, recheck for draws on the system.
Things that you can pretty much rule out from being your draw are Rear defrosters, head lights and the blower motor (although sometimes blower motors can have a low current draw if there is a high resistance short somewhere in them). Light bulbs tend to have about a .3 amp draw, although this can vary depending on bulb size.
Good luck and hope you find it.
Edit: Missed the third page. Even with computer memory functions you should see less than .035 amps. Also, it sounds like the HO2S heater is shorted to ground either internally or in the wiring from the heater circuit back to its control device.