To be sure I answer your question I'm going to give an expanded description of my process. I apologize if I'm over-doing the information.
To summarize: I recirculate continuously throughout the mash and the sparge/wash. Recirculation clears the wort and exposes the enzymes in it to all the grain to increase efficiency.
More information than you may want:
The water bath temperature is controlled by a thermostat, so it will hold the mash about two degrees below the temperature of the water bath. The mash temperature will rise fastest when the difference in the mash temperature and the water bath is greatest. As the temperature of the mash approaches the temperature of the water bath the mash will warm more slowly. Eventually the mash will hold at about 1 or 2 degrees below the temperature of the water bath. Once you have watched the process a couple of times you'll have a feel for how long it takes and can spend that time reading or doing something else around the house.
At the end of the mash, once the water is drained from the BK/water bath (tilt the BK so virtually all the water drains out), I shut off the pump and move the hose that was running from the outlet of the heat exchanger coil to the mash tun so it runs into the BK. I partially close the valve on the outlet side of the pump as soon as the wort drains off the surface of the grain bed. If I leave the valve open all the way, it will start sucking air before all the wort has trickled down to the bottom where it can keep the pump full.
With the first runnings in the BK, I dump the room temperature sparge/wash water into the mash tun and stir. (Now is a good time to stick something under the side of the mash tun opposite the drain so you can drain as much wort as possible later in the process.) My round 10-gallon cooler is not the easiest container to stir; I suspect a rectangular cooler would be easier to stir - oh well, I've already bought it, so it'll just have to suffice. I begin heating the first runnings in the BK; the first runnings are now the "water" in my heat exchanger water bath. Move the heat exchanger outlet hose back to the mash tun and restart the pump. I set the water bath (first runnings) thermostat to about 180 F and recirculate until the mash tun temperature gets to about 170 F, then reset the thermostat to 170 F and continue to recirculate until both the top and bottom of the mash are at 170 F. Yep, I need two thermometers in the mash tun.
Shut off the pump and move the heat exchanger hose back to the BK, restart the pump, and pump the second runnings/sparge/wash into the BK. You won't be able to get everything out of the mash with the pump, so once it starts sucking air, disconnect the hose from the pump inlet and let it drain into another container. Once the last of the wort drains out, or once you're tired of waiting, dump the container into the BK. Now comes the hard part: getting the last bit of wort out of the pump, hoses and heat exchanger coil into the BK. I disconnect the hoses and drain them (easy) then hang the coil upside-down over the kettle; most of the wort will drain out.
Once you think most of the wort has drained out of the heat exchanger coil, or once you get tired of waiting, or at least 15 minutes before the end of the boil, return the heat exchanger coil to the BK so it can be sanitized before you turn off the heat. While the wort is boiling, dump the grain out of the mash tun and clean it, then re-connect the hoses to the heat exchanger coil and fill it with tap water. When you're ready to start cooling, pump tap water through the coil until the wort is under 100 F, then pump the tap water down to just above the outlet and add crushed ice. Continue to recirculate until you hit your pitching temperature. You can also connect a hose from the tap to the heat exchanger coil and run tap water directly through the coil. However you run water through the coil, you'll clean the wort out of it so it doesn't get moldy.
Other odds and ends:
Let the chilled wort sit for 30 minutes to let the hot break, cold break, and hop debris settle before you drain the kettle.
Put a stainless steel scrubber over the outlet of the BK to filter out crud when you empty the BK into the fermenter.
The wort will clear quickly as you drain the kettle, but it will be cloudy for the first few seconds. Catch the first few seconds of wort coming out of the kettle in a container and return that gently to the kettle.
I've heard people refer to stuffing the stainless scrubber into the kettle outlet to keep it in place. I use a tee-shaped piece of copper tubing to wedge it in place. If I don't put it in before I start the heating the water bath at the beginning of the brew session, I usually forget it.
Wedge something under the side of both the BK and the mash tun opposite the outlets to allow more liquid to drain out.
If your tap water is suitable for the sparge/wash water you can scoop water out of the water bath to sparge/wash and avoid having to warm it with the HERMS.
You can pre-heat the mash and sparge/wash water, then use the HERMS to maintain temperature. If you're doing this, you might as well just use Denny's Quick and Easy system (Dennybrew.com).
HERMS is not the fastest way to brew, but with a thermostat to control the heat exchanger water bath it can be automated to the point that you can do other things while the mash is converting and sparging/washing.