Thanks for some more ideas to look at. Fuel filter & plugs have already been replaced with no change. I've opened the gas cap when this happens but I still have the problem. The vent tube inside the tank is pretty soft... so maybe that is collapsing in the heat and causing the problem?
Yesterday was very hot here - mid '90s and the bike sat out in that all day while I was at work. It was pretty hard to start and then had trouble keeping an idle without the choke (throttle advance) on. I kept the choke on much longer than normal so it would keep an idle.
I had just read about the hall effect sensor earlier today and was going to try testing that to see if it's the problem. But it does seem that something is getting effected by the outside ambient temperature and causing an issue.
I tried to park in the shade today...
I have yet to figure out the purpose of the small vent hose coming down from the top of the tank, rear of the filler cap. I assume that's the one you mean. The early bikes didn't have one, and mine runs just fine without it. Probably not your issue.
So, it runs fine, but cranks and cranks before "sputtering" to life? Don't buy a hall sensor yet. I'd expect it to be failing on the road when it gets hot if it were the hall sensor.
This is still reading like a fuel or air problem to me. The sputtering in particular.
Are you equipped to check fuel pressure?
If not (or even if so), you could try pulling the fuel rail and cranking it to check the spray from the injectors. (I'm not sure my hoses would really permit this, but apparently some have been able to do it.)
Have you checked for spark? Pull a spark plug, reattach it to its wire, and rest it on the valve cover (metal rim of plug must contact a grounded surface, which the valve cover is). Crank the starter and see if you can see the spark. Obviously do this before spraying gas everywhere with the injectors.
Elsewhere - these bikes are very fussy about electrical connections, and intermittent heat-related issues are sometimes a matter of a connection that works when cold (or warm) but is compromised when it warms up (or cools down) and things expand/contract out of place. A few prime candidates are the bunch of ground wires under the tank, the main ground connection on the transmission, and the big plug connectors to the EFI box under the seat, and the ignition box under the tank.
When you have things apart and are mucking around, take a moment to disassemble the big cluster of ground wires under the tank, clean each wire's terminal ring (I use 400 grit sandpaper and/or scotchbrite pad and/or sanding sponge), and the main ground point itself. Same with the main ground wire on the transmission. For the two plug connectors, Stabilant 22 is the gold standard contact cleaner *and enhancer* (which is important). People swear by it. I'm cheap, so I use DeOxit, which is available locally and much cheaper. Carefully clean each pin on the box and receptacle in the cable connector. Let dry before reassembling.
Another persistent fuel/electric problem area is fuel pump power, which is delivered through the fuel level sender bolted to the bottom of the tank. Failure points are the four-pin connector under the right rear corner of the tank (clips to the plastic tray down there), and the point where the wires pass through the plate in the bottom of the tank. The ground wire here, which is soldered to the bottom of the plate, is a common culprit. If you think the problem is here, and you can't isolate it to the connector or the external ground connection, the next option is to replace the whole dang thing at about $130.
EuroMotoElectrics sells a nice set of upgraded cables for the starter and main ground, which I think improved my starting. If it sounds like the engine is adequately turning over, this probably isn't your problem, and I think BMW upgraded the ground cable on the bike by '92 as well.
