Prediction of transpiration is important for design and management of ventilation and irrigation systems within greenhouses in warm, semi-arid regions.  The Penman-Monteith (PM) equation is widely used as a basis for modeling field crop evapotranspiration and has been proposed for predicting plant water use in greenhouses. The equation predicts latent heat flux as a sum of radiation [A (R_n-G)] and aerodynamic [B VPD] terms, where R_n is net radiation, G is soil heat flux, and VPD is vapor pressure deficit in air. The radiation and aerodynamic coefficients A and B depend upon plant and environment factors including temperature, leaf area, and surface and aerodynamic resistances. The purpose of this study was to experimentally determine A and B for tomatoes (Lycopersicon esculentum) grown under controlled VPD and air temperature conditions within a greenhouse at the University of Arizona Campus Agricultural Center in Tucson during spring 2003. Plants were grown under either high VPD (~2 kPa) with day/night air temperature range ~ 27/18 ^oC or low VPD ( ~0.8 kPa) with temperature range ~ 24/22 ^oC. Plants were grown in nutrient solution with electrical conductivity (EC) either 2.5 or 8 dS m^-1. Transpiration rates from selected plants grown with either nutrient solution were measured using heat-balance based sap flow gauges, however, reliable data were obtained mainly for plants grown in the EC 8 dS m^-1 solution. Results indicate coefficients A and B were relatively constant during daytime hours. During low VPD conditions the coefficients were on average A ~ 0.5 and B ~ 0.04 W m^-2 Pa^-1.  These are comparable to reported values for tomatoes grown in greenhouses in other locations including northern Europe.