I would try and use differential heating, or one of the other methods suggested by Sheldon Brown's.
I had very good luck with cooling the components, but in your case the aluminum is outside, so you have to heat the whole thing. You can adapt my experience as follows.
Because heating too much will definitely ruin the paintwork, I suggest that you use some sort of large container (I'd say 40 cm long, but it depends precisely on the frame geometry).
- 0 - gather all wrenches/pipes/friends/vice/explosives you are
planning to use to uscrew. Keep them at arm's reach.
- 0.1 - [optional] I usually hammer energically the part that is stuck, perpendicular to the screwing direction. In your case this would be along the BB axis. Should you do so, put the frame on a flat surface,
making sure only the non drive side of the BB touches. Then, making
sure it touches wholly, hammer the cup 5-6 times. This is
(supposedly) meant to break oxide bounds in the threads.
- 1 - put the frame inside the container, making sure the BB is fully under the
container edges. Removing the front wheel and/or placing the
container on a small chair/box will help.
- 2 - now put hot water in
it, until BB is about 1cm under.
- 2.1 [optional] I don't think the mass of the frame will be able to cool the hot water too much, but it really depends on the volume ratio between
frame and water. If you think the water has been cooled significantly
in contact with the frame (and the container) you might change it.
- 2.2 [optional] Depending on whether you had success or not, you might want to put the stuck cup in contact with an ice bag without the
latter touching the aluminum.
- 3 - Take the thing out of the water and
rapidly apply unscrewing force.
I'd go with 0,1,2,3. If you don't have success try adding the optional steps. In 1 you will find additional ideas (e.g. using ammonia, soaking in ice - I had a hard times with pedals vs cranks before learning to let them sit overnight in the freezer!).
I have never tried most of them though.