a 3 gallon batch mashed in a 10 gallon cooler

So I have been working on a plan to brew 3 gallon no sparge batches on my stove. I'm thinking about using my 10 gallon cooler to mash in. I'm sure there will probably be a lot of heat loss due to the empty space and there will be a lot of loss from the dead space under the false bottom. Are there any other issues that I'm not thinking of?

I have a sixtel mash tun that I was using but I removed the bulk head for use with my 15.5 gallon sanke mash tun, I will need to build another.

I was thinking about trying a 2.5-3gal batch inside since it's so cold outside. I also have a 10g MLT, so I was thinking about trying the BIAB (brew in a bag) method since you'll probably only be mashing 5-8lbs of grain (unless you're making a barleywine).

I was thinking of going that route also but I dont want any excess trub. I plan on using these beers as starters.

You should have no problem mashing a no-sparge 3 gal batch in a 10 gal cooler. The biggest difficulty will be to collect all the wort (the bigger the cooler, the greater the loss of wort to the mash tun, generally, which can become significant on small batches).

A couple of suggestions to avoid heat loss:
- preheat the cooler REALLY well before mashing
- you can fabricate a circular piece of insulation from rigid foam that fits inside your cooler just above the mash to reduce the dead air space above (preheat that too!)
- mash pretty thin to maximize the volume in the tun

I do 2gallon/5lb batches like this with no trouble in a large cooler. I don't have a false bottom though, more of a sketchy set up with a dryer screen. I tend to keep adding some hot water along the way to keep my temp up.

thanks for the input,
I know that dead space will be a pain (I think I will get that sixtel up and running before to long)
I have been thinking about about the hot water additions also. I'm thinking I might do a couple of steps 148, 158