Distributed lag (DL) models have been consistently used throughout the years to assess the cumulative impact of multiple days of high heat on public health. DL models, however, are often used on an aggregate level (e.g., city or census tracts) in spite of the fact that the effect of heat on health is individual specific, leading to possible ecological fallacies. To capture more individualized effects of heat on health, we propose a negative binomial regression model where the effect of lagged temperatures is age specific. Utilizing principles of predictive process models, we place appropriate smoothness and decay constraints on the associated DL surfaces. Furthermore, we borrow strength across ages to facilitate the estimation of the age-specific DL function. Using death certificate data from the Texas Department of State Health Services, we show how different ages are impacted by consecutive days of high heat.