Zumbido,
There are hundreds of JM cultivars. Varieties have hardiness ratings all over the map. Ergo, their requirements for dormancy vary as well. The key is to talk to a JM grower about what varieties are suited for a 40-45 degree winter environment and buy a specimen of that cultivar. For the cultivar you already own, ask the grower what the optimum outdoor temperature range is and try to provide that environment for it. Talk to a couple of growers. Check the web.