@IslandLizard I usually add what could be steeping grains to my mash when it wont max out my mash tun, I usually only steep now when the base malt and adjuncts which need mashing are as much as my mash tun can hold by themselves.
So you add the dark wort to the bulk after the boil is completely over. What temp is the "steeping wort" when you add it to the cooling wort? With the temp drop that goes through pasteurization temps might not be complete. I'm sure you've done this enough, though, that you've found that it works.
Maybe I'll try something like this later, add the "steeping wort" at the last 10 minutes of the boil.
Sure, mash tun constraints play a role too in that decision. If that happens often, maybe get a 2nd, larger mash tun. I build mine for $35 from a new 52 qt Coleman cooler, a 2" nipple/bulkhead with stainless washer/silicone ring, a leftover 2-piece stainless valve, and some cpvc pipe and fittings for the manifold.
I sometimes mash in the kettle (step mashes or decoctions) and use the tun only to lauter or hold the resting mash between decoctions. You could dump some in a large pot and mash in the oven (preheated to 150F and turned off).
The dark steeping wort usually sits around for a while. It must have cooled down to around 100-120F, I guess, never measured it. I steep, drain, sparge, drain, sparge 2nd time, and drain again. I'm using a large sieve, no bags. It's usually less than a gallon. Oh, I use 3rd runnings for steeping and sparging liquor, around 1.022 or so.
I turn the plate chiller water and recirculating pump off when I get at 165-170F, hard to hit that precisely. I sometimes have whirlpool hops running at that temp for 15-30 minutes. I then add the black wort and stir. I'm making sure it doesn't drop below 160, holding it there for 30 seconds or so.
Until I understood pasteurization is all that's required, I really prefer to have the dark roasted wort not getting that hot for any length of time. Much smoother and fresher tasting. IMO, 10' in the boil is 20' too hot too long already.