Different populations of organisms occurring across varying thermal regimes show diversity in responses to heat stress. We use a “common garden experimental” approach designed to deal with phenotypic plasticity to study in Lymnaea stagnalis (Linnaeus, 1758) the behavioural and molecular responses to a heat shock in laboratory-inbred snails (W-strain) and freshly collected snails (Stony strain) from ponds. In the W-strain, which has been reared under standardized temperatures for generations, the exposure to 30 °C for 1 h (heat shock, HS) when experienced after a novel “taste” results in a taste-specific aversion known as the “Garcia effect”. This learned avoidance requires the upregulation of heat shock proteins (HSPs). In contrast, freshly collected Stony strain, which experiences temperature fluctuations regularly, does not exhibit a Garcia effect. Here, we found that (1) Stony-strain snails have higher basal mRNA levels of HSPs than W-strain ones; (2) in the W-strain, the training procedure to cause the Garcia effect upregulates the mRNA levels of HSPs and key neuroplasticity-related genes such as CREB1 and GRIN1; (3) in Stony-strain snails, the same training procedure fails to alter the mRNA levels of those targets. These data suggest that Stony-strain snails do not perceive the HS as a stressor because of the higher HSP basal mRNA levels, which may confer a higher thermal tolerance.