At the end of mashing, the temperature of the mash is probably in the low 150's.
When I fly sparge, I add about 1g of near boiling water at the end of the mash to bring the temp up to about 170 before starting the sparge. I also try to keep the sparge water just about level with the top of the grain bed so the water supports the weight of the grain. I also do the same thing when batch sparging, but most people would add hotter sparge water to the first batch to raise the mash temp. (I batch sparge so infrequently that I haven't determined what temp the initial batch should be.) If you keep the sparge temperature at about 170, you will rinse out more sugars than if you sparge at a lower temperature, but if you go much over 170, you run the risk of extracting excess tannins (especially when fly sparging).
I use a 5g Gott cooler with a false bottom. I had a few stuck sparges when I started using it, because I was using it incorrectly.
The following procedures completely got rid of the stuck sparges.
1. When doughing in, always add foundation water before adding any grain. I add water until it is about 2 - 3 inches above the top of the outlet from the false bottom.
2. Drain a small amount of the water out of the spigot before adding any grain. This purges all air from the delivery system and prevents airlocks.
3. Add the grain in small amounts while stirring, and add extra water if the grain is not completely wetted. This helps prevent the grain compacting against the false bottom.
Following these rules, I've mashed with as little as 1 qt per pound, and as much as 1.5 qt per pound, and never had a stuck sparge.
Hope this helps
-a.