No, I don't use a separate mash tun--that's the beauty of BIAB, the boil kettle is the mash tun. Just lift the bag, the wort stays behind, boil away.
I wrote about the temp issues in my previous post. Some of this is empirical, i.e., you simply need to find some reasonable starting values for temps, and see what you get.
Further, and I didn't write this in the previous post, you'll want to insulate the kettle during the mash so as to hold temps. I use a sort of a quilt-type thing to wrap my kettle to hold heat. Pic below. Some use a sleeping bag, some use reflectix insulation, there is a bunch of options.
Additionally, there's no "mash out" where you quickly increase the temp of the mash to denature the enzymes. I've never done that. I can see where in a commercial brewing setup you might need to do that to maintain consistency, but not in what we do. No need.
Here's what I do: Strike temp at 159 or 160; grain bill about 11 or 12 pounds. I bring the water to the strike temp in the kettle. I'll make sure it stabilizes at my temp, stirring to ensure the heat is evenly distributed through the water. I brew on a Hellfire burner so there's some retained heat in that burner, so I wait a couple minutes for that residual heat to make it into the kettle.
Once I'm happy w/ the water temp (takes maybe 5 minutes, it's not rocket science), I'll put the bag in, stretching it out around the mouth of the kettle and cinching it tight. Then in goes the grist. Don't worry about the bag not fully expanding initially--the grist will take care of that. I slowly pour in the grist, gently stirring as I do to incorporate the grist into the water. Too fast and I'll get dough balls which will float. You'll always get some, just press them against the side of the kettle to break them up.
Then, once I've got the grain incorporated, I add the kettle lid and cover it up and wait. At 15 and 30 minutes, I'll unwrap, stir, and rewrap. I also check pH at 15 minutes or a bit later, but you don't have to do that. If you have a good water spreadsheet (Brunwater or EZwater), you'll probably be OK with that.
At the end of 60 minutes, I hoist the bag, start the burner heating the wort, and squeeze out what I can. Then wait for the wort to come to a boil.
Voila! I find BIAB to be simpler and more relaxing than traditional mash tun. YMMV.
