Spring (March to May) and autumn (September to November) are invariably the best times to visit Jordan, when temperatures are not too hot or too cold.
The summer months (particularly July and August) can get insufferably hot, especially in the Jordan Valley where it gets very hot and humid, as well as the desert. Temperatures are regularly upward of 36C.
In winter it can get surprisingly cold. Sometimes snow falls in Amman, and even Petra on occasion. In the desert the nights are especially cold in winter. Aqaba is the exception though, with temperatures averaging around 20C in January, making it a popular destination for a spot of winter sunshine.
Be aware when you travel of the month of Ramadan (usually around June and July) when there are restrictions in place on eating, drinking and smoking in public.