The rich dynamics of analog oscillators can be controlled to solve Non-deterministic Polynomial-time hard problems by mapping the Ising model to a network of coupled oscillators. Low-power analog oscillators are good candidates to efficiently implement Ising spins thanks to their parallel computing capability. Such as, oscillators based on vanadium dioxide material (VO2) are often considered as they allow a compact and low-power hardware implementation operating at room temperature. However, as both electrical and thermal variables characterize VO2 devices, it is essential to understand the impact of temperature on OIM performances before implementing such hardware at large scale. In this work, we study an OIM with oscillating spins based on crossbar VO2 devices and coupled by capacitors. Via TCAD and circuit simulations, we investigate how the external temperature impacts the performances of the VO2-OIM when solving NP-hard MAX-CUT problems. We show that a 10-spins OIM can undergo an 75% accuracy variation due to a 5% external temperature variation only. Our electro-thermal study suggests that VO2 thermal properties should be considered when designing VO2-OIMs and eventually could be harnessed for thermal annealing.