Previous work has shown that environmental variables affect SARS-CoV-2 transmission, but it is unclear whether different strains show similar environmental responses. Here we leverage genetic data on the transmission of three (Alpha, Delta and Omicron BA.1) variants of SARS-CoV-2 throughout England, to unpick the roles that climate and public-health interventions play in the circulation of this virus. We find evidence for enhanced transmission of the virus in colder conditions in the first variant selective sweep (of Alpha, in winter), but limited evidence of an impact of climate in either the second (of Delta, in the summer, when vaccines were prevalent) or third sweep (of Omicron, in the winter, during a successful booster-vaccination campaign). We argue that the results for Alpha are to be expected if the impact of climate is non-linear: we find evidence of an asymptotic impact of temperature on the alpha variant transmission rate. That is, at lower temperatures, the influence of temperature on transmission is much higher than at warmer temperatures. As with the initial spread of SARS-CoV-2, however, the overwhelming majority of variation in disease transmission is explained by the intrinsic biology of the virus and public-health mitigation measures. Specifically, when vaccination rates are high, a major driver of the spread of a new variant is it’s ability to evade immunity, and any climate effects are secondary (as evidenced for Delta and Omicron). Climate alone cannot describe the transmission dynamics of emerging SARS-CoV-2 variants.