A fast analytical calculation method is developed for the thermal design and rating of multi-fluid mixed-mixed cross-flow heat exchangers. Temperature dependent heat capacities and heat transfer coefficients can iteratively be taken into account. They are determined at one or two special reference temperatures. Examples are given for the application of the method to the rating of special multi-fluid multi-pass shell-and-tube heat exchangers and multi-fluid cross-flow plate-fin heat exchangers. The accuracy of the method is tested against numerical calculations with good results.