"Cool" is best for Bok Choy.
Since baby leaves and young leaves are delicious, you could start them for salad as late as 3 weeks before frost (and most varieties do tolerate a little light frost).
Some varieties are fully mature by 35 days, and some big ones take 50 days to reach full size (5-7 weeks).
Most varieties quote 40-45 days to maturity (6 weeks), but that's not assuming 19 hours of sunlight!
I think you could still get a fully mature crop even if your first fall frost was as early as August 1 or 8.
They say that Chinese cabbage (like Napa and Michihli) likes shortening day length. Maybe it would like Alaska?
