Once varicose veins or extraneous veins are treated, the blood returns to its normal physiology - norma pressures, flow etc without pooling in redundant veins (unnecessary veins). So, treating varicose veins IMPROVES venous physiology, venous flow, venous pressures, etc.
When temporal veins are removed, blood will flow through other veins which are called collateral veins. There is no change in the rate of blood return to the heart or in the caliber of the remaining veins. As with any veins, there is always the chance that new veins can form.