Ba0.63Sr0.37TiO3 (BST) films were first deposited on SiC substrates with LNO bottom electrodes by magnetron sputtering. The BST/LNO/SiC thin films exhibit high dielectric tunability and low dielectric loss while maintaining excellent temperature coefficient of dielectric constant in the temperature range between 250 and 350K. We also investigated the effect of film thickness on the dielectric properties. BST(430nm)/LNO/SiC film has higher tunability (68.09% @700 kV/cm), lower loss tangent (tan=0.00987) and quite a bit higher figure of merit (FOM=68.99) as compared with that of BST(300nm)/LNO/SiC film. Our results demonstrate that combining ferroelectric BST films with SiC substrates is very promising for the development of tunable devices over a large temperature range.