We consider the extension of the Schwarzschild metric to a counterpart that can describe an extended spherically symmetric stellar body with acceptable density distribution, and with a thermal profile. With a length parameter, apart from the Schwarzschild radius, the proposed metric can fit the values of density, pressure, and temperature, at the stellar surface, and give a complete profile down to the core. Such a metric extension seems to describe a central core with an "energy-producing, explosive core", as well as an inflationary "coronal windy layer", two regions where the mean pressure seems to acquire negative magnitudes. Our illustrative computations and graphical illustrations refer to the sun as a reference example. We discuss the Schwarzschild limit of such metrical model. We also discuss the interior gravitational potential and its repulsive central core.