I've only tried this setup once, but I tried to keep my sparge water at 180F (82C). Then recirculating through that was sufficient to bring my mash temp up to the 168-170F (76C) range for mashout. It might be worth mentioning that my temp probe is near the bottom of my grain bed, so I actually turn off the pump at 168F since the top of the mash is probably closer to 170.
I then turn off the sparge water heat and start letting it cool, but start fly sparging with the 180F (82C) water. I figure it is trickling in slow enough during a fly sparge that it will cool on the trip over to the mash tun and on making contact with the 170F mash. Since the usual goal is to leave an inch or 2 of water above the grain bed during a fly sparge, I figure even if the water in that top fraction of an inch is a couple degrees over 170F, it isn't in contact with the grains anyway.
That said, I usually don't even bother with a mash out. I just did it once because I had to to a step mash for a witbier, so had the recirculation pump and coil set up anyway.