The convective motion of water in a small cylindrical container, where the bottom and walls are heated and maintained at a constant temperature and heat is removed from the top surface, has been studied numerically. The no-slip condition is specified at the water–air interface to simulate the effect of a thin absorption film. A temperature wave, which rotates in parallel to the surface at an angular velocity of (0.06 ± 0.02) rad/s, has been detected for the first time in this system. This wave is high-mode, has a frequency of about 0.1 Hz, and is observed in very narrow ranges of the dimensions of the container and temperatures.