The thermal stability of a resistive, force‐free plasma in a two‐dimensional, slab geometry is investigated numerically. Linearly unstable modes that arise as an energetic consequence of Ohmic heating are examined in relation to the dynamic magnetic‐tearing instability. Plasma compression is found to give rise to a set of unstable thermal modes not seen in previous incompressible studies. Such modes can occur in parameter regimes where no purely growing tearing mode exists.