El-Cheapo TPS can be had for as little as $60.00 or so from your local parts house, the Delco ones are going to run you somewhere in the neighborhood of $125.00 or so.  Installing isn't too bad but a code reader or multi-meter is required to set it properly and it has a very small tolerence to work properly. A 1982 service manual will give you the settings and if you dont have one, I can look it up and send it to you.  On your crossfire system, the problem could also be from the Idle Air Controllers (IAC) that screw into the front of each throttle body.  If the plunger isnt working properly (or the ECM compter is giving it wrong information) it won't adjust the proper amount of air into the throttle body.  If you have done any work in the area of the throttle bodies, check the connections to each IAC and to the TPS. I had the same  problem about a year ago with my crossfire and found that it was a ground problem.  There are grounds on the top of the intake and I believe two big grounds under the chassis, one to the passengers side of the transmission and another main ground under the battery.  Check and clean any grounds that don't look good, a bad gound can affect how the ECM operates.  Cleaning the grounds solved my problem.  DO NOT attempt to adjust the idle screws on the throttle bodies unless you REALLY know how to do it... that's why they were welded in place and capped at the factory.  One reason that crossfire got a bad rep was "mechanics" trying to adjust and balance the throttle bodies without knowing how to do it.  It can be done but there is a proper procedure for doing it, I have a link somewhere if you need it but it AINT real simple to do.  If you suspect an IAC is bad, you can buy or borrow one, ($50.00 - $100.00, depending on make) and swap it from one throttle body to the other, they are interchangable. The chances of both of them going bad at the same time is almost non-existent.    Be careful inserting the IAC onto the throttle body, being careful not to damage the seat inside of the TB, IACs are cheap, throttle bodies are not.  The same IAC that fits your car fits lots of GM cars and is readily available so a mechanic friend may have one laying around you could test with. A code reader can tell you what the ECM is telling the IAC to do but it can't tell you if the IAC is actually doing what it's told.  The connection for the code reader is under the ash tray, pull the ash tray out and it's staring at you.............long answer to a short question.  I'd be interested if other 82 owners have had this same problem and how they handled it.

My idle will oscillate between 1200 and 800 RPM when I first start up. After about 10 seconds it settles down at around 800 RPM.

Be sure to check for vacuum leaks as well, I dont know why a leak would stop leaking after a few minutes of running , but a vacuum leak will give a high idle as well.