Extreme heat events can lead to increased risk of heat-related deaths. Furthermore, urban areas are often hotter than their rural surroundings, exacerbating heat waves. Unfortunately, validation is difficult; to our knowledge, most validations, even if they control for temperatures, really only validate a social vulnerability index instead of a heat vulnerability index. Here we investigate how to construct and validate a heat vulnerability index given uncertainty ranges in data for the city of Rio de Janeiro. First, we compare excess deaths of certain types of circulatory diseases during heat waves. Second, we use demographic and environmental data and factor analysis to construct a set of unobserved factors and respective weightings related to heat vulnerability, including a Monte Carlo analysis to represent the uncertainty ranges assigned to the input data. Finally, we use distance to hospital and clinics and their health record data as an instrumental variable to validate our factors. We find that we can validate the Rio de Janeiro heat vulnerability index against excess deaths during heat waves; specifically, we use three types of regressions coupled with difference in difference calculations to show this is indeed a heat vulnerability index as opposed to a social vulnerability index. The factor analysis identifies two factors that contribute to >70% of the variability in the data; one socio-economic factor and one urban form factor. This suggests it is necessary to add a step to existing methods for validation of heat vulnerability indices, that of the difference-in-difference calculation.