This is pretty impossible. But I did find a couple things. First is the Climate Predication Center’s three month outlook for the entire US just click on the “three month outlook” for temp or precip. From what it looks like, they are predicting equal to normal temps and equal to normal precip. This website can give you past climatological information. For example, select “preliminary monthly climate data”, some location (central park?) and under “timeframe”, choose “archived data, and the month of June last year to give you an idea of the temps from last year. The New York State climate office may have some good info, too. But remember, this is for all of New York, so you may have to bum around the site for a while to find any climate information.