We study the effect of synthesis temperature on the phase formation in nano(n)-SiC added bulk MgB2 superconductor. In particular we study: lattice parameters, amount of carbon (C) substitution, microstructure, critical temperature (Tc), irreversibility field (Hirr), critical current density (Jc), upper critical field (Hc2) and flux pinning. Samples of MgB2+(n-SiC)x with x=0.0, 0.05 & 0.10 were prepared at four different synthesis temperatures i.e. 850, 800, 750, and 700oC with the same heating rate as 10oC/min. We found 750oC as the optimal synthesis temperature for n-SiC doping in bulk MgB2 in order to get the best superconducting performance in terms of Jc, Hc2 and Hirr. Carbon (C) substitution enhances the Hc2 while the low temperature synthesis is responsible for the improvement in Jc due to the smaller grain size, defects and nano-inclusion induced by C incorporation into MgB2 matrix, which is corroborated by elaborative HRTEM (high-resolution transmission electron microscopy) results. We optimized the the Tc(R=0) of above 15K for the studied n-SiC doped and 750 0C synthesized MgB2 under 140 KOe field, which is one of the highest values yet obtained for variously processed and nano-particle added MgB2 in literature to our knowledge.