Wild bill, lets answer this backwards.
Use enameled winding wire, you are not going to need many turns so there will be plenty of room. I use multipul strands, much easier to wind and get looking neat.
Refer to this site for current ratings for a given wire size,
http://www.powerstream.com/Wire_Size.htm
For low batteries the current is limited by a combination of winding wire resistance but mostly the voltage, this is where to much volts and therefore amps,quickly overheats the winding. (remember volts is equal to pressure in water while amps is equal to flow)
I believe you will need close to 15-17 turns, based on your first post you have an AC volts/turn of 0.81, so 15 turns gives you 12.15V AC. DC 15.8V (12.15V AC X 1.4 - 1.2V( bdidge diodes) which should be adequate. The benefit of matching the volts to your ideal finish volts 15.5V DC, is the current should reduce to a trickle when the battery is fully charged.
So taking some voltage losses in the windings I would wind two strands of #18 gauge for 15 turns. Bring a loop out, do another winding, bring a loop out then another, finishing on the 17th. If you need more just soilder the ends and put on more windings. You will have plenty of room so wind three if you wish, the windings will run cooler.
Now each of these loops sticks up the side of the coil forming a tapping point giving you some choice allowing you to tune the output current.
Please wind them at once, if you wind seperatly be very sure the number of turns are equal, and wound the same direction.
The temperature of the transformer in operation is predomintly from heating in the windings, yes ambient does make a difference but not as much. It does not want to be enclosed in an unvented case, but clearly safetly enclosed.
For the purists yes there are more factors to take into account in transformer design but not in this case.
allan down under