There are a number of sensors (6 or 7 I think), but I don't know where they are all located. I would really appreciate an annotated photo if someone can put one together. I know there is one in the SATA cable that goes to the hdd, and I know there is one on the heat-sink.
I have a similar problem/symptom on my MacBook Pro 13" ... (which was given to me). I don't think it suffered water damage but rather shock damage.
After replacing the hdd with an ssd, and replacing the broken glass, the only remaining problem was that the CPU was being throttled, presumably due to a heat problem. However, what was encouraging was the throttle problem was intermittent. So, whilst trying find more info about this, I came across www.ifixit.com and posted there. They suggested I change the hdd SATA cable since it wears from heat over time. I was sceptical and decided to take mine to Mac Doctors first. Their diagnosis didn't sway me either way (since they just wanted to replace sub-assemblies for $$$), and so I decided to order the cable and see. Their delivery was good, but replacement of the cable, in my case, didn't fix my problem. So I went and bought some heat transfer compound, and will do the CPU/GPU heat-sink when I get some info about the other sensors.
In spite of what Matt says, where he is essentially paraphrasing what the industry wants you to believe, once you find the component, it is quite possible to replace it, even when its a SMT device. (Not every device has dozens of tiny pins.)
As I don't know where all the other sensors are, I can't say whether they're integrated into a component (like the SATA cable) or whether they're stand-alone components.
Either way, Apple would have purchased the sensors from someone, so getting a replacement will be a matter of finding a supplier from whom you can make a purchase. (Which would be made easier if you can identify somehow; who the manufacturer is and what the part number is.)
Another possibility is to get a board that's failed for some other reason, and cannibalise it.
As far as soldering, SMT soldering gear is affordable. What you need beyond a normal solder iron, solder and flux; is a stand with a good light, a magnifying glass, some means of holding the board steady, and a solder tip with a sharp point. Some practice of the technique before you attack your computer would be handy.
All in all, if you can't fix the existing board, it will be cheaper to purchase another Mac, 2nd hand as I don't think getting it repaired is economical considering the quotes I got from Mac Doctors last week.