Acoustic travel time tomography is presented as a possibility for remote monitoring of near surface air temperature and wind fields. This technique provides line-averaged effective sound speeds changing with temporally and spatially variable air temperature and wind vector. The effective sound speed is derived from the travel times of sound signals which propagate at defined paths between different acoustic sources and receivers. Starting with the travel time data a tomographic algorithm (Simultaneous Iterative Reconstruction Technique, SIRT) is used to calculate area-averaged air temperature and wind speed. The accuracy of the experimental method and the tomographic inversion algorithm is exemplarily demonstrated for one day without remarkable differences in the horizontal temperature field, determined by independent in situ measurements at different points within the measuring field. The differences between the conventionally determined air temperature (point measurement) and the air temperature determined by tomography (area-averaged measurement representative for the area of the measuring field 200 m x 260 m) were below 0.5 K for an average time of 10 minutes. The differences obtained between the wind speed measured at a meteorological mast and calculated from acoustic measurements are not higher than 0.5 m s^-1 for the same averaging time. The tomographically determined area-averaged distribution of air temperature (resolution 50 m x 50 m) can be used to estimate the horizontal gradient of air temperature as a pre-condition to detect horizontal turbulent fluxes of sensible heat.