Australia's Bureau of Meteorology calculates apparent temperature like this

AT = Ta + 0.33×e − 0.70×ws − 4.00

where:

Ta = Dry bulb temperature (°C)

e = Water vapour pressure (hPa) [humidity]

ws = Wind speed (m/s) at an elevation of 10 meters

The vapour pressure can be calculated from the temperature and relative humidity using the equation:

e = rh / 100 × 6.105 × exp ( 17.27 × Ta / ( 237.7 + Ta ) )

where:

rh = Relative Humidity [%]

http://www.bom.gov.au/info/thermal_stress/#atapproximation