Some thoughts: You say your high end temps are 80-90. Not knowing what kind of heat source you are using....try to make your hot end temps more stable and in the low 90's. I think he may not be warm enough overall and it may have affected his appetite. The outside weather there should not be a factor in what "HIS" temps are. His cool end temps should be a little warmer also. He may have the beginnings of an RI from the cool temps....perhaps a visit to the vet is in order.
Some suggestions that have worked for me: I thaw my F/T out in warm water and let them soak a little. Just before I feed, I run very warm water over them so that the mouse is warm to the touch. He may need to "feel/sense" the heat radiating from the mouse for a strike. Sometimes babies need to have the mouse dangled and wiggled a little. I have also had babies that feed better in a darkened room. If you're feeding during the day, turn out the overhead lights. This will also keep him from seeing you as well, thus eliminating distractions. Also, try leaving the mouse in his enclosure overnight on the warm end. It may also be that he will need a few more feedings of live prey before he will convert to F/T. That is certainly preferable to allowing him to become malnourished and weak. That's all I can think of right now from the information you provided. There are a couple of things you could try tubing him with later on to stimulate his appetite if all else fails, but you should talk it over with your vet and do it as a last resort. If the feeding tips don't work in the fairly near future, I would take him to a reptile vet. You should be able to find some good ones in Houston. I know some experienced herpers in the Houston area, that could suggest a good one for you and may even help you with your baby. Email me privately at lindah@thegrid.net if the feeding tips don't work.