Pierce's disease (PD) of Vitis vinifera grapevines is caused by the bacterium Xylella fastidiosa, a pathogen with a wide plant host range. Exposure of X. fastidiosa-infected plant tissue to cold temperatures has been shown to be effective at eliminating the pathogen from some plant hosts such as grapevines. This "cold curing" phenomenon suggests itself as a potential method for disease management and perhaps control. We investigated cold therapy of PD-affected 'Pinot Noir' and 'Cabernet Sauvignon' grapevine. In the fall, inoculated plants and controls of each cultivar were transported to each of four field sites in California (Foresthill, McLaughlin, Hopland, and Davis) that differed in the magnitude of cold winter temperatures. A model for progression of the elimination of plant disease in relation to temperature was conceptualized to be a temperature-duration effect, where temperatures below a particular threshold kill X. fastidiosa with increasing efficacy as the temperature decreases to some value < 6 degrees C. The temperature effect was modeled as a likelihood of a particular temperature killing the pathogen and is termed the "killing index". We developed a mathematical model for cold curing of grapevines inoculated with X. fastidiosa and calibrated the model with cold-curing data collected in a field study. Parameter estimation resulted in lowest sum of squared differences across all 10 trials to be low temperature below which the organism is killed (T0) == 6 degrees C, number of hours to achieve 100% cure (N100) == 195 h, number of hours to achieve 10% cure (N10) == 20 h, and killing index (Kx) == 0.45 for Pinot Noir and T0 == 6 degrees C, N100 == 302 h, N10 == 170 h, and Kx == 0.41 for Cabernet Sauvignon. With the parameter estimates optimized by model calibration, the simulation model was effective at predicting cold curing in four locations during the experiment, although there were some differences between Hopland for Pinot Noir and Davis for Cabernet Sauvignon. Using historical temperature data, the model accurately predicted the known severity of PD in other grape-growing regions of California, suggesting that it may have utility in assessing the relative risk of developing PD in proposed new vineyard sites.