Annealing undoped MgB2 wires under high isostatic pressure (HIP) increases transport critical current density (Jtc) by 10% at 4.2 K in range magnetic fields from 4 T to 12 T and significantly increases Jtc by 25% in range magnetic fields from 2 T to 4 T and does not increase Jtc above 4 T at 20 K. Further research shows that a large amount of 10% SiC admixture and thermal treatment under a high isostatic pressure of 1 GPa significantly increases the Jtc by 40% at 4.2 K in magnetic fields above 6 T and reduces Jtc by one order at 20 K in MgB2 wires. Additionally, our research showed that heat treatment under high isostatic pressure is more evident in wires with smaller diameters, as it greatly increases the density of MgB2 material and the number of connections between grains compared to MgB2 wires with larger diameters, but only during the Mg solid-state reaction. In addition, our study indicates that smaller wire diameters and high isostatic pressure do not lead to a higher density of MgB2 material and more connections between grains during the liquid-state Mg reaction.