Numerous studies have highlighted the merits of grafting to improve the performance of vegetable crops. However, the technique is hindered by several obstacles, including the synchronization of seedlings used as scions and rootstocks, and the effects of rootstocks and climatic conditions on grafting success rates. This study sought to gain insights into how such technical obstacles affect tomato grafting. An initial experiment conducted in a greenhouse set out to assess the relevance of using degree-days to predict the growth rates of seedlings used for grafting (i.e., stem diameters above cotyledons). The success rate for grafting a tomato variety (Tanya) on 10 different rootstocks from different species—namely tomato, eggplant, african eggplant, and a wild species—was assessed at different temperatures (i.e., 15, 20, 25, 30, 35, and 40 °C). The effects of grafting on plant vigor (i.e., fresh biomass), number of leaves, and plant height, and on the hydraulic conductivity of xylem vessels in the plant stem were assessed 2 weeks after grafting. The results show the advantage of using degree-days to predict the ready-to-graft stage of seedlings, as it reduced the discrepancy among trials. The grafting success rate was more than 90% at 15 and 20 °C, but decreased significantly with higher temperatures, down to 20% at 40 °C. Larger variations in growth rate for seedlings used as scions and rootstocks, a lower grafting success rate, and less vigor were recorded for heterografted plants than for homografted plants. The lower hydraulic conductivity measured in the stems of grafted plants, especially heterografted plants, was consistent with the lower plant vigor observed. Further studies are needed to investigate how grafting affects the hydraulic conductivity of xylem vessels in later developmental stages of grafted plants.