Water Bath Temp

I have searched a bit, but can't find a good answer that I am looking for, if someone has a link please post.

I am looking to ferment about 65 to 70 degrees to start a Kolsch. Looking to put it into a water bath in the basement closet in an old fish tank. If I am looking to get about 65 in the fermentor that is in the water bath, what temp should the water in the fish tank be to balance it out?

So I am currently thinking about how to go about doing this same thing. My best guess is that you can assume that the thermal mass of the wort will be about the same or slightly higher that the water you want to use.

Therefore if you have 10 gallons of water in the bath and 5 gallon batch of wort/beer at 75 degrees you would take the difference between actual and desired temp (75-65=10.F) and then half that because you have 2x the amount of chilling water. By this simple calculation you are talking about 10 gallons of 60'F h20 bringing 5 gallons of 75'F wort to 65'F.

This is neglecting the heat of the carboy and the increased thermal mass from the higher gravity of the wort as well as the heat generated by the yeast metabolism. You might want to try err on the cold side then? (58'F?) and have ice ready.

This is what I have reasoned out, I would also appreciate any more thorough/rigorous insight.

I do this in large rubbermaid tubs, probably like 20 gallons. The temperature of the stick on thermometer is very close 2-3 degrees from the water temp. I usually fill the water about 2/3 of the way up the bucket, with the thermometer just above the water line. If the tank is fairly large, it will act as a very efficient heatsink, and you could aim for the bath water to start right around low 60s and then move it up to upper 60s. If you are doing a big beer or one with a very vigorous fermentation, I might want to go as much as 5 degrees below target.

Water baths are also good to make any temperature rises slower than they otherwise would be. If you had one beer ferment in a room temperature water bath, it wouldn't reach the same peak temp as one fermented without a bath. So even if you have trouble keeping a certain bath temperature, the bath will help to lower any temperature spikes.