Volatile resistive switching in correlated-electron systems, characterized by an abrupt resistance decrease under applied current, is crucial for developing next-generation electronics. Despite its technological significance, the underlying physics remains elusive. Inorganic thin films on substrates—the widely studied platform for resistive switching—usually exhibit broad temperature-induced metal-insulator transitions (MITs) and substantial heat dissipation. These factors complicate the nonlinear thermal effect induced by Joule heating, a key contributor to resistive switching, rendering it excessively complex and difficult to decipher. Here we investigate a resistive-switched state in the bulk organic conductor (d7-DMe-DCNQI)₂Cu, which undergoes an extremely sharp first-order MIT and exhibits weak heat dissipation, using resistance and ¹H-NMR measurements. These extreme conditions make the Joule heating effect vivid, allowing us to observe peculiar phenomena, including temperature locking to the MIT and `inverse Ohm's law'---an inverse proportionality between voltage and current. These findings provide fundamental insights into the nonlinear thermal effect in resistive switching, offering a pathway to efficient resistive-switching technologies.