Proverbially, "even a broken watch is right twice a day."
That's a thought I have every time I hear someone ask (or answer) about the mash out. In most cases, the answer I hear invokes some discussion of "do it, because raising the temperature decreases viscosity." It is sometimes then followed by, "but be careful not to make it too hot, or you'll get lots of tannins."
In this case, our broken watch is probably only right once a day. You probably should go ahead and do a mash out. And you should probably not be all that concerned about what you raise the mash temperature to.
Fire it Up
Let's start with the "hot lautering/sparging will make your beer astringent" thing.
First off, tannin extraction depends on a hell of a lot more than just the temperature in the mash tun. Among those factors a central feature is the pH of the mash. Simply put, assuming you're in the "normal" pH range (5.2-5.8) for a brewing mash, it's not much going to matter if your temperature in the tun gets about 170F/77C.
One reason I feel confident saying this is that, just for kicks, I brought my mash up to 180F/82C for several consecutive batches, and there was no change in the resulting beers based on organoleptic analysis in blind judging. I used my most-common recipes for things like Altbier, Porter, and Bitter, and the resulting beers tasted as they usually do, scored as they usually do in competition. Heck, the Bitter was one of the most-reliable and best-scoring versions I've ever made (I have a semi-infamous love-hate relationship with that style, in that it's easily in my top three favorites but I have historically struggled to produce high-scoring versions).
Second, it's harder than you might think to get your mash up that high in the first place. I perform a modified no-sparge method that entails adding one big ol' mash out addition in more or less identical volume to a batch sparge, and I had to have that sucker at near-boiling to raise the existing mash and wort to 180F/82C. "Accidentally" raising the temperature in there too high would take some effort, like "accidentally" emptying the dishwasher when you were trying not to.
Don't fear the heat.
Physics v. Physics
Then there's the vaunted "viscosity" argument. That's one that I bought into myself, before someone who knows much more about this than me explained to me that I had been completely snookered. It involved words I didn't completely understand, but the gist was that since we weren't talking about dissolving sugar into the liquid, the temperature didn't make a difference once conversion had already occurred. The sugar is there. It's in the liquid. It's not being washed off of the grains. As a result, the viscosity of sugar at varying temperatures doesn't much matter.
Having said that, we can pivot to a physics term I actually do understand, especially as I once toyed with the idea of majoring in astrophysics: time. Mashing out won't do anything meaningful to the viscosity of your mash, but it does require you wait a few minutes before moving on. In that simple passage of time, you're potentially allowing for a bit more conversion and/or some increased efficiency due to marginal pH change, either of which will lead you to the false-positive conclusion of, "AH, See! I increased the temp in the mash, which made the wort less viscous, and therefore I got more sugar!" No, you almost certainly got more sugar because you made more, not because you melted it into solution by raising the mash temperature.
Wrong and Right
So, when it comes to the mash out addition, we're wrong about a lot of it, but still getting the right result. It's dumb, but we should still do it.
First, it'll get you a few more gravity points, so why not?
Second, even though it entails waiting another few minutes, it's time you're saving when you run off and come to a boil, because the resulting liquid is that much warmer already.
Just don't come at me with all that viscosity talk.
Keep it simple.
Please help support BEER SIMPLE by visiting the Support page and saving the links there as your bookmarks, especially this Amazon link! Every dollar you spend will help keep BS coming your way, and more often (which is at least as much a threat as a promise).