We present a novel method to analyze the local current-voltage I-V characteristics of both solar cells and cell precursors. The method, which we call "Suns-ILIT", is based on illuminated lock-in thermography (ILIT) measurements and photoluminescence imaging (PLI) in open-circuit conditions with varying illumination intensities. Compared to conventional techniques for the determination of local solar cell parameters, the advantage of Suns-MIT lies in the high accuracy while imposing minimal requirements on the sample. In particular, no electrical contact to the sample is needed. We derive the necessary equations from the contributions to the power dissipation and investigate the impact of the Peltier heating and cooling on the final outcome. The method is applied to a standard multicrystalline silicon PERC solar cell for demonstration.