I plan to go taiwan on betweeen end of sept 2015 and beginning of oct 2015.

This place always welcomes you with its pleasant seasons. It typically presents an average temperature of 22C (71.6F) all year round. The average temperatures of Sept. and Oct. respectively are 79 °F and 73 °F. It's comfortable. It's a good time to visit.
But June to October is the typhoon season. You should bring your rain gears.