Potato is a globally important, highly heat-susceptible crop species. We investigated the effects of prolonged exposure to elevated temperatures and exogenous salicylic acid (SA) on microplant growth and heat-shock response (HSR) in three unrelated potato genotypes/cultivars. Long-term exposure to 29 °C (mild heat stress) caused a significant reduction in the number of surviving explants and shoot morphometric parameters in heat-sensitive genotypes, while exposure to 26 °C (warming) caused only a decline in shoot growth. Interestingly, 26 °C-temperature treatment stimulated root growth in some investigated genotypes, indicating a difference between favorable temperatures for potato shoot and root growth. SA showed a protective effect regarding potato shoot growth at 26 °C. At 29 °C, this effect was genotype-dependent. SA did not affect the number of roots and inhibited root elongation at all temperature treatments, indicating the difference between shoot and root responses to applied SA concentration. Although HSR is mainly considered rapid and short-lived, elevated transcript levels of most investigated HSFs and HSPs were detected after three weeks of heat stress. Besides, two StHSFs and StHSP21 showed elevated expression at 26 °C, indicating extreme potato heat-susceptibility and significance of HSR during prolonged warming. SA effects on HSFs and HSPs expression were minor and alterable.