Electromagnetic radiation in the terahertz (THz) frequency band has unique potential for future communication and imaging applications. However, the adoption of THz technologies is hindered by the lack of cost-effective THz sources. Here we demonstrate a way to generate and control THz radiation, via spatio-temporal emissivity modulation. By patterning the optical photoexcitation of a surface-passivated silicon wafer, we locally control the free-electron density, and thereby pattern the wafer’s emissivity in the THz part of the electromagnetic spectrum. We show how this unconventional source of controllable THz radiation enables a form of incoherent computational THz imaging. We use it to image various concealed objects, demonstrating that this scheme has the penetrating capability of other THz imaging approaches, without the requirement of femtosecond pulsed laser sources. Furthermore, the incoherent nature of thermal radiation also ensures the obtained images are free of interference artifacts. Our spatio-temporal emissivity control could enable a family of long-wavelength structured illumination, imaging, and spectroscopy systems.