We work in a building built of cinder block which stays cold and damp most of the year. At this time the building is getting ready for an addition to be constructed which means we have no heat in the office, there's a cold breeze blowing through there at this time. There aren't any holes in the walls or anything at this time. I was born and raised in south Florida, so I can sympathize with your feelings about 62 degrees. OSHA doesn't have a specific rule on heating.
Many people work outdoors in the cold.
Government regulators believe that someone could bundle up in 62 degree weather and stay warm. There are probably extreme cases in which the authorities may respond. You might ask if you can bring in a space heater, although some employers don't want the fire risk. It sounds like your new building may be your only hope. I have been working in the roofing business for about 20 years.