161F is really too high if you want decent conversion out of a single infusion mash. I would NOT rely upon stirring alone to get the temp down if you hit 158F or higher.
Beta amylase is quickly denatured at or above 70C (158F) -this is worse if you're using highly modified, low enzymatic power (DP) malt such as English malt and is also worse if you generally have a thin mash. -You need to get that temperature down FAST; I'd recommend the ice route without delay.
It's not a big deal, you can still make great beer, but you won't make the beer you were shooting for. Pale malt's beta amylase has already taken a hit during the longer kilning process; a hot infusion in a thin mash will denature the beta amylase in a hurry.
-Also adding water to your grain instead of adding grain to your water will prevent the enzymes from being over heated during mash-in; if you store your malt in a cold garage -bring it inside the night before you brew so that the temperature difference between your malt and your water is lower and your strike temp is correspondingly lower (again meaning that the malt is hit with less intensely hot water at mash-in). -This is even more important if using English pale malt again, not just because of the lower enzymatic power but also to avoid getting dough-balls as Marris Otter is pretty famous for gnarly dough balls when using really hot water.
Adam