Heat Index is an important measure in determining the safety of temperature conditions for humans. Extreme heat can lead to dangerous, even deadly, health consequences, including heat stress and heatstroke. Thus, there is a need to predict the Heat Index accurately in order to warn individuals about such conditions so that they take appropriate precautions. In this paper, we look at weather data in Mumbai from 2008 to 2020 and attempt to come up with predictive models for the Heat Index. We carry out feature selection first in order to efficiently use a variety of algorithms to develop predictive models. We use various mathematical techniques such as Multiple Linear Regression (MLR), Simple Exponential Smoothing (SES), Artificial Neural Networks (ANN), and Auto-Regressive Integrated Moving Average (ARIMA) models to predict the heat index. The experimental results are evaluated and compared using the Root Mean Square Error (RMSE). On experimenting with all four models, it was discovered that the ARIMA model yields the best predictive model having an RMSE of 0.354654 on testing data. This model is also concluded to be optimal as the residuals of this model are a gaussian white noise. Furthermore, the poor performance of MLR indicates that temperature cannot be accurately modeled through a linear function of the variables considered.