Disclosed is herein an air hypocaust structure for cooling and/or heating dwellings. In winter, hot air is supplied into a space between an upper and a base plate constituting the air hypocaust structure to heat the dwelling according to a convection and a radiation mechanism. In summer, cold air is supplied to the space between the upper and base plate to cool the dwelling according to the convection mechanism. A plurality of support legs and guide plates are installed between the upper and base plate, and the support legs and guide plates may be integrally formed on the lower side of the upper plate or may be separately produced to be assembled with the upper plate. A hole is formed at a lower end of each of the support legs, and projections each having a sharp tip at an end thereof and corresponding in position to the support legs are formed on the upper side of the base plate. Therefore, when the upper plate is assembled with the base plate, the sharp tips of the projections are inserted into the holes of the support legs to firmly assemble the upper plate with the base plate. Furthermore, the guide plates are arranged between the upper and base plate to control the direction of a hot or cold air current flowing through the air hypocaust structure.