Information technology has a great demand for magnetoresistance (MR) sensors with high sensitivity and wide-temperature-range operation. It is well known that space charge inhomogeneity in graphene (Gr) leads to finite MR in its pristine form, and can be enhanced by increasing the degree of spatial disorder. However, the enhanced MR usually diminishes drastically as the temperature decreases. Here, by stacking a van der Waals ferromagnet Fe₃GeTe₂ (FGT) on top of graphene to form an FGT/Gr heterostructure, we demonstrate a positive MR of up to ~9400% under a magnetic field of 9 T at room temperature (RT), an order of magnitude larger MR compared to pure graphene. More strikingly, the giant MR of the FGT/Gr heterostructure sustains over a wide temperature range from RT down to 4 K. Both control experiments and DFT calculations show that the enhanced MR originates from spin-dependent orbital coupling between FGT and graphene, which is temperature insensitive. Our results open a new route for realizing high-sensitivity and wide-temperature-range MR sensors.