Extreme weather affects the timing and intensity of infectious outbreaks, the resurgence and redistribution of infections, and it causes disturbances in human-environment interactions. Environmental stressors with high thermoregulatory demands require susceptible populations to undergo physiological adaptive processes potentially compromising immune function and increasing susceptibility to infection. In assessing associations between environmental exposures and infectious diseases, failure to account for a latent period between time of exposure and time of disease manifestation may lead to severe underestimation of the effects. In a population, health effects of an episode of exposure are distributed over a range of time lags. To consider such time-distributed lags is a challenging task given that the length of a latent period varies from hours to months and depends on the type of pathogen, individual susceptibility to the pathogen, dose of exposure, route of transmission, and many other factors. The two main objectives of this communication are to introduce an approach to modeling time-distributed effect of exposures to infection cases and to demonstrate this approach in an analysis of the association between high ambient temperature and daily incidence of enterically transmitted infections. The study is supplemented with extensive simulations to examine model sensitivity to response magnitude, exposure frequency, and extent of latent period.