i don't know about 40 degrees...maybe 60-65 degrees. personally, i wouldn't keep a betta (or any fish) in a bowl. i just see this as a stressful life, not merely because of the tiny size, but also because of the potential stress involved with massive, frequent water changes.
i have a blue gourami quarrantined in a 3g eclipse. i don't think this is good for the fish, but it is necessary at the moment. the fish is actually doing fairly well in that unheated, but filtered tank. however, i do live in florida, so the ambient temp in my apartment never drops below 70, and is usually between 74-77. most gouramis get too large to really consider them good for bowl-sized tanks...larger than bettas, in any case.
but...when i think about it, i suppose one *could* keep a single dwarf in a bowl and have it *survive*. i just don't think it would flourish. of course, i'm not sure that bowl-bettas *flourish* either.