Degenerate optical parametric oscillators (OPOs) divide optical frequencies by two with only modest pumping, making them promising mid-infrared frequency comb sources. Our measurements show that our degenerate OPO preserves the frequency comb stability of the pump to sub-Hz levels. However, degenerate OPOs are often overlooked due to their interferometric cavity stabilization requirements. We find that the stability requirements of our system are actually much simpler, because thermal feedback results in self-stabilization. When the OPO is oscillating, absorption of the intracavity field increases the crystal temperature, and subsequently the effective cavity length, which is fortunately the right direction to stabilize degenerate oscillation in our system. Our OPO is based on an orientation-patterned GaAs crystal, pumped by a stabilized 2 W, 418 MHz, optically-referenced Tm frequency comb, generating a broadband, midinfrared frequency comb centered at 4 μm. We have observed continuous OPO oscillation for almost an hour without cavity length feedback. These measurements show that a degenerate OPO can serve as a simple device to downconvert a frequency comb.