In this work a theoretical analysis was made on the influence of the temperature density relationship on natural convetion heat transfer in the region of maximum desity. An Isothermal sphere immersed in water was considered in this study. Using boundary layer simplifications and similarity transformationhs, thecontinity, momentum, and energy equations which are non linear and depend on the boudary conditions. These symultaneous differential equations, which describe the velocity and temperature of the sphere as well as the water. The sotution of these equations gives twotypes of flow regimes; the first, the common unidirectional one., and the second, a bidirectional one, in which there is flow reversal. In both of theases regimes of the sphere and water. The principle objective oh this study was to abtain the variation in the heat transfer coefficient wich is dependent on the velocity field, wich in turn is dependent upo the temperatures of the sphere and water. Since the maximum desity of water occurs at 3,98 Celsius degrees, the temperature of the water in this study was varied between 0 Celsius degrees and 20 Celsius degrees, while the temperature of the sphere was varied between 0 Celsius degrees and 35 Celsius degrees. Numerical results were obtain with the use of the IBM-1130 and 370 computors at Rio Datacentro of PUC.