Heat stress is an increasing challenge for production animals, particularly in warmer regions of the world. The aim of this study was to compare the fit of three different relationships when modelling respiration rate (RR) and rectal temperature (RT) in animals exposed to increased load. Data from three published studies on finishing pigs, gestating sows and dairy cows were analysed. RR and RT are characterized by being unaffected by increased heat load as long as it is kept below a certain level, and in warmer conditions they increase with increased heat load. As an expression of heat load either the air temperature or the ET (Effective Temperature) was used. The ET unites the effect of air temperature, air humidity and velocity on the animal perception of increased heat load. The relationship between RR and RT and the temperature or the ET was analysed by multiple change point regression and the cubic relationships were modelled. In general, the models provided better fits for RR compared to RT. Relationships with an unaffected piece followed by a quadratic relationship and the cubic relationships performed nearly equally well. Using ET resulted in better correlations than using temperature alone for gestating sows and dairy cows.