The greenhouse whitefly Trialeurodes vaporariorum Westwood (Hemiptera: Aleyrodidae) is a serious pest of many fruits, vegetables and ornamental crops in sub-tropical regions and in greenhouses worldwide. Potato is a secondary host of the species but the major threat from this insect in the Andean region for potato is the transmission by this insect of a crinivirus causing Potato yellow vein disease. Determination of the pest’s temperature-dependent population growth potential is crucial knowledge for understanding the population dynamics and spread potential of the species and the diseases it can transmit, as well as for designing effective pest management strategies. Trialeurodes vaporariorum development, mortality and reproduction were studied at seven constant temperatures ranging from 10 to 32 °C. The Insect Life Cycle Modeling (ILCYM) software was used to fit nonlinear equations to the data and establish an overall phenology model to simulate life-table parameters based on temperature. In addition, life tables of T. vaporariorium were established at daily fluctuating temperature in two different environments: Cusco (5 °C–35 °C) and La Molina, Lima (13.7 °C–24.9 °C), and used to adjust and validate the model. The insect only completed its life cycle at constant temperatures above 15 °C and below 32 °C although the cycle was completed at daily fluctuating temperatures between 5 °C and 35 °C. The overall model portrayed population development within the temperature range of 14° to 32 °C with a maximum finite rate of population increase (= 1.14) at 23 °C. However, the model revealed poor convergence with life tables established at fluctuating temperatures indicating an influential effect of temperature fluctuations on the whitefly life history parameters, particularly on adult survival time and reproduction. Therefore, we adjusted the model for convergence with a single life table observed at fluctuating temperature. The adjusted model gave good predictions when compared with remaining observed life tables and published data. The adjusted model predicted population development within the temperature range of 11.5 °C–35.5 °C, and maximum population growth at around 24 °C with a finite rate of increase, λ, of 1.137 and a population doubling time of 5 days. The established process-based physiological model presented here for T. vaporariorum can be used for predicting the species distribution potential based on temperature worldwide and should prove helpful in adjusting pest management measures. Moreover, the information obtained will be used to predict the spread potential of potato yellow vein disease.