Yup, it does. But if it is fuel related, it likely will get worse.
Check around fullsizechevy.com for the same failure mode, there were a LOT of TBI 350's in the trucks. Lurk around impalassforum.com too, again, lots of TBI's in the 90-93 B/D Body cars too. Even the L03 is similar (the 305 version). The 454 (L19) is similar as well, so don't discount the tips on those engines, they are all a very similar system. Try
http://www.thirdgen.org/techboard/tbi/ too, they had TBI's too (L05's even!)
If you can datalog, you can definitely see more too. It is more advanced thing to do, (not sure how technical you get), it costs around $50 to get into it. Have to see for sure if the L05 can be datalogged.
ECM's for these cars are cheap, so DO NOT get into spending much on them. If you pull yours out (not sure where it is in that car, the LT1 it is behind the left front headlight under the air cleaner) and send me the PN I can look around. You can check my first place, car-part.com. I don't think that is it, so do rush off to replace parts. ECM's are temp sensitive like this at all, I don't think that is it at all. I don't like tossing parts at a problem that isn't fully understood.
It strikes me as fuel related, probably the pump or the regulator. Most likely the regulator.
Try some reading here:
http://www.thirdgen.org/techboard/tb...check-out.html
Look down at fuel pressure regulator....