The very high speed of collapse of cavitation bubbles is responsible for a number of phenomena of interest in science and engineering: Luminescence, sonochemistry, cavitation damage, ultrasonic cleaning, etc. Strongly forced bubbles may collapse with such violence that the relatively slow processes of diffusion of the heat of compression and of excess vapor to the bubble wall are obviated. This leads to an approximately adiabatic system with nearly constant mass during the final stages of extreme collapses, accompanied by the evolution of sharp thermal and compositional boundary layers on either side of the interface. It is shown that the boundary layers, which are involved in the determination of the interfacial temperature through the balance of sensible and latent heats, may profitably be described mathematically through integral equations. This complements well the boundary integral solution of the fluid dynamics, which has been the basis of much progress in the field.