The cooling of the center of mass motion of optically trapped microspheres by feedback stabilization is advancing rapidly, and cooling below several millikelvin is possible. Such a controllable attenuation of the motion is an important step towards new experiments in different areas of physics. In this study we suggest going in the opposite direction, in controlling the motion of optically trapped spheres, namely, to increase the amplitude of their Brownian fluctuations. We show that the effective kinetic temperature of a Brownian particle may achieve 3000 K when an additional external random force is applied to the sphere. We demonstrate experimentally how the temperature increase affects the histogram of the position of the Brownian particle, its power spectral density, its response to an external perturbation, and the statistics of the Kramers transitions in a double-well potential. Effects related to the nonideal character of the white noise generated experimentally are also analyzed. This experimental technique allows tuning and controlling the kinetic temperature of the sphere with millisecond resolution over a wide range and along a single spatial direction, and has considerable potential for the study of thermodynamic processes at the microscopic scale.