The occurrence of extreme heat events in maximum and minimum daily temperatures is modelled using a non-homogeneous common Poisson shock process. It is applied to five Spanish locations, representative of the most common climates over the Iberian Peninsula. The model is based on an excess over threshold approach and distinguishes three types of extreme events: only in maximum temperature, only in minimum temperature and in both of them (simultaneous events). It takes into account the dependence between the occurrence of extreme events in both temperatures and its parameters are expressed as functions of time and temperature related covariates. The fitted models allow us to characterize the occurrence of extreme heat events and to compare their evolution in the different climates during the observed period. This model is also a useful tool for obtaining local projections of the occurrence rate of extreme heat events under climate change conditions, using the future downscaled temperature trajectories generated by Earth System Models. The projections for 2031-60 under scenarios RCP4.5, RCP6.0 and RCP8.5 are obtained and analysed using the trajectories from four earth system models which have successfully passed a preliminary control analysis. Different graphical tools and summary measures of the projected daily intensities are used to quantify the climate change on a local scale. A high increase in the occurrence of extreme heat events, mainly in July and August, is projected in all the locations, all types of event and in the three scenarios, although in 2051-60 the increase is higher under RCP8.5. However, relevant differences are found between the evolution in the different climates and the types of event, with a specially high increase in the simultaneous ones.