Which quince? Chaenomeles? or Cydonia? Or Pseudocydonia? Flowering, European fruiting, or Chinese fruiting quince?
All are in the apple family, most are USDA zones 7 to 4, a few can get by in zone 8. There's a reason apples are not grown in southern Florida, it is too warm in winter.
If the chill requirements are not met, the new growth will either be late or won't happen. Usually 32 to 40 F is recommended as the warmest you want to try to meet chilling requirements with. You "might" be able to meet requirements with your temperatures. It might take longer, or it might not work at all. Perhaps someone from Florida or Southern California can weigh in. Given the number of Chaenomeles photos I've seen from So. California, Chaenomeles might be okay with it. Don't know about the others.