Current leads are the key components which make an electrical connection between room temperature power supply and superconducting magnets at 4.2 K. In any cryogenfree magnet system, major heat input comes from the copper current leads of the magnet. The dimensional optimization of the copper part of the hybrid current leads is done for a particular operating current between room temperature to the operating temperature of the 1 st stage of cryocooler (CCR). The conduction-cooled magnet may not necessarily be operated at the optimized current all the time. Hence for non-optimum current, the heat input per unit current will be increased both at under-current and over-current operation. The stabilized temperature, of the 1 st stage of CCR corresponding to each operating current, would mainly be governed by the dynamic heat input by the current lead. A pair of copper current leads working between the temperatures 300 K to 33 K has been optimized for 85 A optimum current. A simple analytical technique has been used for estimation of dynamic heat load at non-optimum operation. This paper describes the optimization procedure, estimation of dynamic heat input, measurement and detailed thermal analysis of conduction-cooled current leads at non-optimum operation.