Jordan has a typically Middle Eastern climate in which summers are very hot, with temperatures reaching up into the forties celsius. If you are not adversely affected by heat it is still worth considering a trip at this time as you will have sights like Petra almost to yourself.
Spring and autumn are the best times to travel as the days are warm, with temperatures into the high twenties celsius with cool nights.
Winters can be surprisingly harsh: Petra has sometimes experienced snow, and the nights get cold especially in the desert regions. Winter is also when the majority of the rain falls, but showers tend to be short and sharp.