The purpose of this project is to extend the Heston model in order to incorporate the term structure (TS) of the implied volatility surface. This includes implementing a TS within the Heston model and its calibration to a set of market instruments. The TS Heston model with piecewise constant parameters is implemented to match the TS and the COS pricing method is used for fast option pricing. We calibrate the model to the EUR/USD and USD/JPY market data and historic data is also used to test the robustness of the model. Then the model with calibrated parameters are used to price exotic options by means of Monte Carlo simulation with a new control variate we propose. Finally we also propose the COS method for pricing discrete barrier options as future research directions.