Yep, cold is what asparagus needs to go dormant and stay that way. You might want to put ice on top of the soil or something, just to cool off the soil around the plants and try to keep it cold. Then make some shade for the area, too, so the sun doesn't warm the soil up again if we have a run of sunny weather. Set up some shade cloth, or park some big potted plants on the south side of the asparagus bed?
I'd think the north side of a building would be a good place to try to grow asparagus in Florida. At the very least the shade from the building would keep the soil cooler through the winter months. I plant my daylilies on the north side of the house for the same reason - to give them as much winter chill as possible.
