When I batch sparge, I sparge with whatever temperature water I need to bring my grain bed to 168. I don't do a mashout, so my first sparge addition is usually around 200. The second one is usually 170, since the grain bed is already at 168.
Mash out is adding water to the grainbed/liquor to bring the entire contents to 168 before the sparge. This is more common in fly sparging, but it's done with some batch sparging techniques, especially if they do a mash out and then only one additon of sparge water. After the mash out liquid is added, the first runnings are drawn off.
I don't mash out when I batch sparge. I drain the MLT first. Then, I stir in the first batch sparge water amount (1/2 of the entire sparge amount). That's drained off completely, and the second round of batch sparging is started.
When I fly sparge, I usually mash out, or at least use the HERMS to bring up the temperature of the grainbed.