Local weather influences the transmission of the dengue virus. Most studies analyzing the relationship between dengue and climate are based on relatively coarse aggregate measures such as mean temperature. Here, we include both mean temperature and daily fluctuations in temperature in modelling dengue transmission in Dhaka, the capital of Bangladesh. We used a negative binomial generalized linear model, adjusted for rainfall, anomalies in sea surface temperature (an index for El Niño-Southern Oscillation), population density, the number of dengue cases in the previous month, and the long term temporal trend in dengue incidence. In addition to the significant associations of mean temperature and temperature fluctuation with dengue incidence, we found interaction of mean and temperature fluctuation significantly influences disease transmission at a lag of one month. High mean temperature with low fluctuation increases dengue incidence one month later. Besides temperature, dengue incidence was also influenced by sea surface temperature anomalies in the current and previous month, presumably as a consequence of concomitant anomalies in the annual rainfall cycle. Population density exerted a significant positive influence on dengue incidence indicating increasing risk of dengue in over-populated Dhaka. Understanding these complex relationships between climate, population, and dengue incidence will help inform outbreak prediction and control.