This paper addresses the estimation problem of temperatures and reaction heat within an intensified heat exchanger/reactor (HEX reactor) from the available temperature measurements, namely the input and output temperature measurements. This estimation is performed by a high gain cascade observer incorporating a suitable saturation function to deal with the peaking phenomena which will referred to as a suitable high gain cascade observer (SHGCO). This observer has been developed from a recent research activity devoted to the high gain observer engineering features bearing in mind promising modelling results of the HEX reactor involving a cascade of sub-reactor models. The effectiveness of the proposed SHGCO has been illustrated throughout relevant simulation results with particular emphasis on the estimation accuracy and the remarkable peaking phenomenon reduction during transition periods.