Tomato spotted wilt (TSW) is a serious constraint to tomato production in various regions of the world. The effect of TSW on tomato yield is largely influenced by time of infection. Early infection usually results in severe stunting of the seedling and even death of the plant. Plastic mulches have been found to affect both the incidence of TSW, and plant growth and yield of tomato. The objective of this study was to determine the effect of root zone temperature (RZT) as affected by plastic mulch on the timing of appearance of first TSW symptoms, vegetative top fresh weight (FW) and fruit FW in tomato. Under natural TSW infection as well as in artificially inoculated plants, vegetative top FW and fruit FW were both linearly related with number of days after transplanting (DAT) the plants were free from TSW symptoms. The plants grown on black mulch during the fall showed earlier appearance of TSW symptoms, and had significantly reduced vegetative growth and fruit yields. The mean RZT during the first 42 DAT—the time before the plants reached full canopy closure—significantly affected the timing of first appearance of TSW symptoms, tomato plant growth and fruit yield. Vegetative top FW (optimal RZT = 24.1 °C) and fruit FW (26.9 °C) fitted the quadratic relationships with the mean RZT during the first 42 DAT. In conclusion, utilization of plastic mulches that created conditions of RZT stress, particularly heat stress, resulted in reduced plant growth and yield and may predispose the plants to earlier expression of TSW symptoms compared to plants grown under RZTs more favorable to tomato plant growth.