I would add a bit to what Darin said as I actually have that cuisinart ice cream maker.

1. When I freeze the bowl overnight in the chest freezer I have had no problems with any mix regardless of fat or sugar content; it gets very cold.

2. The quality is better when the mix has been chilled but room temp mix still works well enough when I'm out of time (and ice).

As for churning time, I follow the manufacturer's instructions which if I recall is 30-35 min and it has always turned out correctly. It is still soft at that point and needs to be hardened in the freezer but that is the way it is supposed to work.