Apple iMac Hardware Test Error 4SNS/1/40000000: TG0D-11.500

My 2009 iMac has been acting strangely for a few months. I noticed that the fan seemed to be running fast and noisy. At first I just ignored it, thinking that maybe iMacs just ran hot. But after a while I sensed something wasn't right, and I looked into what was normal fan behavior. With the help of the iStat widget, I discovered my fan speed was staying consistently over 3500 rpm. Normal fan speeds are around 1400rpm for iMacs. Something was wrong.

More research uncovered that Apple has a hardware diagnostic test for their Macs. To run it, you shut down your computer, restart the computer, and quickly press and hold the letter D (you've got to press the key immediately after hitting the power-on button). Running the test revealed the following error: 

4SNS/1/40000000: TG0D-11.500

I haven't called Apple to confirm exactly what it is, but researching similar error codes suggest it has something to do with my iMac's temperature sensor. It's likely faulty. I found a temporary fix in resetting the Mac's System Managament Controller (SMC). The process is super easy. Apple has instructions on their site, but I'll paste them below (instructions are for iMacs and Mac Pros):

1. Shut down the computer. 
2. Unplug the computer's power cord.
3. Wait fifteen seconds.
4. Attach the computer's power cord. 
5. Wait five seconds, then press the power button to turn on the computer.

It had an immediate effect on my computer. Usually upon restarting my computer, the fan would immediately start running at 3500rpm. This time, it ran at 1000rpm for a minute or so. Unfortunately, the fan slowly revved up to 3600rpm again. I will be taking my iMac in to the Genius Bar to see what they say. Hopefully it is not a logic board issue, as they can be extremely expensive to repair (like $800+).