Weather doesn't make the rut come any sooner or later. The rut will be during the same 10 days (+/- a day or two) each year. Weather will effect how "frisky" they feel meaning vocalization and activity. But the fact is, daylight hours and esterous cycles cause the rut. Calves must be born during a certain time slot in the spring for a high survival rate.
But to answere your question, Sept, 13th-22nd.
Note. This is the "peak" rut times. There are always a few that will hit early and a few that hit late.