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A theoretical treatment of distributed electro-thermally induced intermodulation distortion is developed for microstrip transmission lines. The growth of passive intermodulation distortion (PIM) along the length of a line is derived accounting for both loss and electrical dispersion. PIM dependencies on width, length, thickness, and substrate parameters are analyzed leading to design guidelines for low distortion lines. Single metal silver transmission lines are fabricated on sapphire and fused-quartz substrates to isolate the electro-thermal effect and validate the model. Electro-thermal PIM is measured in a two-tone test with tone separation ranging from 4 Hz to 10 kHz.