Averages for Rome in May. Weather lowdown. May is a fantastic time to visit Rome, Italy, when the weather is warm and dry. At this time of the year, the average temperature begins at 15°C and gradually increases to 20°C as the month progresses.ay is a fantastic time to visit Rome, Italy, when the weather is warm and dry. At this time of the year, the average temperature begins at 15°C and gradually increases to 20°C as the month progresses.