The simultaneous imaging of magnetic fields and temperature (MT) is important in a range of applications, including studies of carrier transport, solid-state material dynamics, and semiconductor device characterization. Techniques exist for separately measuring temperature (e.g., infrared (IR) microscopy, micro-Raman spectroscopy, and thermo-reflectance microscopy) and magnetic fields (e.g., scanning probe magnetic force microscopy and superconducting quantum interference devices). However, these techniques cannot measure magnetic fields and temperature simultaneously. Here, we use the exceptional temperature and magnetic field sensitivity of nitrogen vacancy (NV) spins in conformally-coated nanodiamonds to realize simultaneous wide-field MT imaging. Our "quantum conformally-attached thermo-magnetic" (Q-CAT) imaging enables (i) wide-field, high-frame-rate imaging (100 - 1000 Hz); (ii) high sensitivity; and (iii) compatibility with standard microscopes. We apply this technique to study the industrially important problem of characterizing multifinger gallium nitride high-electron-mobility transistors (GaN HEMTs). We spatially and temporally resolve the electric current distribution and resulting temperature rise, elucidating functional device behavior at the microscopic level. The general applicability of Q-CAT imaging serves as an important tool for understanding complex MT phenomena in material science, device physics, and related fields.