I thought I'd add a picture to illustrate measuring and controlling the water bath temperature. If I measured the carboy temp, this would look like an earthquake.
In this you can see at the starting point I was at 74 F, which is the best I can get with 72 F water until temps cool the ground water later this fall.
I try to get it cooled as quickly as possible. Once the internal carboy temp dropped to 66 F, I set the temperature controller to my target.
My target temp was 65 F. During peak activity, I've found the carboy temp stays along the peaks of the water bath temps. It reaches around 65.25 F as an average high.
Once active fermentation is over, the carboy temp tends to drift down to the midpoint of the water bath cycles. At this point I set the temp controller one degree higher, to keep the temp closer to the 65 F target.
Overall though, we're talking much less than a degree drift when measuring and controlling the water bath temp as opposed to the carboy temp.
This all happens within 48 hours. Incidentally, this is WLP380 pitched cold, after a four day crash cool so I could decant it without losing too much of the low floc portion. 1.052 OG. Shake method aeration. Took off quickly.