No doubt the best period to plan a bike trip in Italy and in Southern Europe is spring and fall, from April till end of October.
In the last 10 years global warming changed a lot our relationship with weather and forecast.
Prediction is a gamble, a wager.
Also we have new phenomena such as sudden increase or decrease of temperature – so in any period of the year you need to bring a rain jacket and something to cover up – and be able to undress – all during a 4 hour riding
Italy: best months to plan a bike trip in Tuscany, Umbria, Puglia, Piedmont and Sardinia are April, May, June, September and October. The same for Dordogne in France and Mallorca in Spain. In those months the weather is almost perfect: sunny, warm but not too much hot, is possible ride all day.
July and August can be hot, in the central part of day is not suggested to cycle.
We usually arrange bike tours but is better be prepared to plan the cycling in the morning, enjoy the hotel with pool in afternoon and visit villages before dinner
On the other hand if you are thinking at Dolomite or FrenchAlps plan the trip end of June, July and August.