Mesa 10 Day Weather. 1  Wednesday:The Mesa forecast for Mar 22 is 75 degrees and Overcast. There is 37 percentage chance of rain and 4 mph winds from the South-Southwest. 2  Thursday:The Mesa forecast for Mar 23 is 61 degrees and Sunny. There is 46 percentage chance of rain and 10 mph winds from the Southwest. Friday:The Mesa forecast for Mar 24 is 72 degrees and Sunny. There is 25 percentage chance of rain and 3 mph winds from the West.