Suggest you get a hold of the 1937 Ford Book published by the Early Ford V-8 Club. It lists all the 'fresh air' or hot air heater options that were available as Ford accessories. So, that means that although your South Wind heater could be installed, it was not the authorized heater for a 1937 Ford.
You can order the book from
www.earlyfordv8.org You do not need be a member to order, but the reference and information would be worth the membership.