The "convection" blower you mention is for the HEAT into the room, has nothing to do with the exhaust.
I think you mean a Direct Vent or Power Vent, those stoves then can be run just about anytime with any temp. and no tall chimney is required, just a vent to outside, it keeps a constant draft on the stove. Not all stokers have Power/direct vents, you can get them either way.
Our Keystoker was a power vent, but since we moved, I hooked it directly up to the brick chimney in the basement and unhooked the power vent.
As long you have a tall enough chimney and good draft, you can light it normally 60 and below, normally the cooler, the better, but we have had our running for over 2 weeks and it was up into the 60's without any draft issues. It is a very tall chimney almost 3 story chimney.