I'm not sure what the actual trigger is, but I think it's more likely day length than temperature. We are growing C. cordata in Hawaii, as well as a number of other Curcumas, and they all go dormant here during winter, which seems to surprise a lot of local people who are not used to that sort of thing.

Interestingly many are native to S.E. Asia, where the winters not only are not cold, they also tend to be dry, with most of the rain in the summertime. Here, on the other hand, the winters are wet and the summers dry, but that doesn't seem to alter the dormancy cycle any, it just makes them a bit more prone to rotting.

Curcuma, globba, zingiber, schomburkia, and siphonochilus are all deciduous gingers. They go dormant in the dry season and re-emerge after the monsoon season in their native habitats. This happens to coincide nicely with the summer/winter cycle in the US