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Since temperature extremes have a strong impact on environment and society, it is crucial to understand their underlying mechanisms. While their relationship to the large-scale atmospheric circulation has been comprehensively investigated, the role of physical processes in the formation of air masses with extreme temperatures is less well understood. This study presents a Lagrangian analysis of the 0.1% most extreme six-hourly hot and cold events in three European regions (UK, Central Europe, Balkans) for the time period 1989-2009. The results provide insight into typical transport patterns and physical processes (adiabatic compression, radiation, surface heat fluxes) occurring along the trajectories of extreme temperature air masses. Cold events in Europe are most frequently induced by advection of cold air masses from the Arctic and Russia. The transport to the target region is characterized by a temperature increase caused by adiabatic compression and, in the maritime setting of the UK, also by diabatic heating due to surface sensible heat fluxes. Despite the warming along the trajectories, the extremeness of the associated 2 m temperature increases, due to the dislocation of the air mass to regions with a milder climate. Hot events are generally associated with weaker horizontal transport, but strong adiabatic warming and local temperature increase caused by enhanced radiation and surface heat fluxes. This in situ warming is particularly strong in Central Europe. Evaluating the temperature evolution along the trajectories reveals that hot and cold extremes develop on a similar time-scale of 2-3 days. This time-scale is mostly set by physical processes for hot extremes and controlled by advective transport for cold extremes. The diagnostics applied in this study lead to an improved process understanding that can provide a basis for more accurate predictions of temperature extremes. [ABSTRACT FROM AUTHOR]