The total energy of a magnet in a magnetic field is lowest when the magnetic moment is aligned parallel to the magnetic field. Once aligned, the magnetic moment can be reversed by applying a sufficiently large field in the opposite direction. These properties form the basis of most magnetic recording and storage devices. But the phenomenon of magnetization reversal in response to a change in temperature (in a small magnetic field) is rarer. This effect occurs in some ferrimagnetic materials consisting of two or more types of antiferromagnetically ordered magnetic ions, and forms the operational basis of ferrimagnetic insulators. Here we report the observation of multiple temperature-induced magnetization reversals in YVO3. The net magnetic moment is caused by a tilting of the antiferromagnetically aligned moments of (crystallographically identical) V3+ ions, due to orthorhombic distortion in the crystal structure. We observe an abrupt switching at 77 K associated with a first-order structural phase transition, and a gradual reversal at ~95 K without an accompanying structural change. The magnetization always reverses if the crystal is cooled or warmed through these two temperatures in modest fields. We propose a possible mechanism involving a change in orbital ordering which may be generic to a broad class of transition metal oxides.