Fast Simulation of Electro-Thermal MEMS provides the reader with a complete methodology and software environment for creating efficient dynamic compact models for electro-thermal MEMS devices. It supplies the basic knowledge and understanding for using model order reduction at the engineering level. Emphasis is placed on the application of the Arnoldi method for effective order reduction of thermal systems. This tutorial is written for MEMS engineers and is enriched with many case studies which equip readers with the know-how to facilitate the simulation of a specific problem.