We are now over seven months into a pandemic of COVID-19 caused by the SARS-CoV-2 virus and global incidence continues to rise. In some regions such as the temperate northern hemisphere there are fears of "second waves" of infections over the coming months, while in other, vulnerable regions such as Africa and South America, concerns remain that cases may still rise, further impacting local economies and livelihoods. Despite substantial research efforts to date, it remains unresolved as to whether COVID-19 transmission has the same sensitivity to climate and seasonality observed for other common respiratory viruses such as seasonal influenza. Here we investigate any empirical evidence of seasonality using a robust estimation framework. For 304 large cities across the world, we estimated the basic reproduction number (R0) using logistic growth curves fitted to cumulative case data. We then assessed evidence for association with climatic variables through mixed-effects and ordinary least squares (OLS) regression while adjusting for city-level variation in demographic and disease control factors. We find evidence of association between temperature and R0 during the early phase of the epidemic in China only. During subsequent pandemic spread outside China, we instead find evidence of seasonal change in R0, with greater R0 within cities experiencing shorter daylight hours (direct effect coefficient = -0.247, p = 0.006), after separating out effects of calendar day. The effect of daylight hours may be driven by levels of UV radiation, which is known to have detrimental effects on coronaviruses, including SARS-CoV-2. In the global analysis excluding China, climatic variables had weaker explanatory power compared to demographic or disease control factors. Overall, we find a weak but detectable signal of climate variables on the transmission of COVID-19. As seasonal changes occur later in 2020, it is feasible that the transmission dynamics of COVID-19 may shift in a detectable manner. However, rates of transmission and health burden of the pandemic in the coming months will be ultimately determined by population factors and disease control policies.