Using a simplified equation of state, an analytic solution for the temperature, pressure, velocity, and acceleration of two semi‐infinite liquids initially at two distinct temperatures is obtained by ignoring the effects of the generated pressure on the temperature distribution. It is found that the pressure wave generated in the cooler medium by the temperature discontinuity develops into a shock after passing through the thermal boundary layer. The cooler material is initially accelerated into the hotter material and thus if the cooler material is lighter, the interface is Raleigh–Taylor unstable. The pressures and velocities at the interface relax with a characteristic time &tgr;=&agr;/c2, where &agr; is the thermal diffusivity andcis the speed of sound. For the particular case of liquid Na in contact with liquid UO2specific results are given. The linearized approximation is compared with exact numerical integration of the full hydrodynamic equations and reasonable agreement is found.