Stability and tuning characteristics of continuous-wave optical parametric oscillators (CW OPOs) are affected by various thermal effects arising from optical absorption in nonlinear crystals. In this paper, we present an experimental study of such effects in a singly resonant CW OPO. The OPO operates in the 3-μm mid-infrared region and it is based on a MgO-doped periodically poled lithium niobate crystal. We focus our study on two thermally induced phenomena that have been recently reported to exist in singly resonant CW OPOs: optical bi-stability and thermal self-locking. Thermal self-locking effect, which is known to alter the stability and tuning properties of doubly and triply resonant CW OPOs, is shown to be also of importance in singly resonant OPOs. We report the stability and tuning characteristics of a thermally loaded OPO and discuss a simple temperature-tuning method that can be used to scan the OPO idler frequency continuously over several THz.