This small post isn't so much for the regulars here, it's more for a consumer to find Googling some day, wishing to repair a fault such as this one had. This is an Accurite Model 00782.
The problem was that the outdoor temp was displaying ~106 F in a room that was nowhere near that temperature (should have been near 80 F). I have had this for years and I noticed it gradual displaying too high a temp for the outdoor sensor.
After changing the batteries, and not changing the results, I decided to take apart the outdoor sensor. Upon inspection I found that some compound had "grown" between some unused SMD jumper pads, probably causing an error in the reading. I scrubbed the area with alcohol and removed the chemical growth. That fixed the problem. It's certainly back within specifications for such a consumer device which is probably +/- 10% or so.
So, for you out there that aren't familiar with trying to fix electronics, you might consider taking apart the item you are about to throw away, and simply inspect it. Stick to small battery powered items like this one and other things such as toys. Hey it's worth a try isn't it?