With the current progress of superconducting integrated circuits, circuit complexities have reached more than 100,000 Josephson junctions. At the laboratory environment, circuit tests are generally being conducted at liquid Helium environments. With the commercialization of the superconducting integrated circuit-based systems and/or price increase of liquid Helium, utilization of the closed-cycle systems will be inevitable. Even though it is possible to implement closedcycle systems with quite substantial excess cooling powers after all the wirings and peripheral circuits, one point notto be overlooked is the power density at the superconducting chips. We have observed that the circuits designed for operation at liquid Helium bath have much higher power densities that exceed the heat flux capacities of closed-cycle cryocoolers. We have measured that the heat flux capacities of closed-cycle systems are about 0.1 W/cm2 when the chip is in vacuum. Thus, if the power density in any of the bias resistors are higher than these values, it is difficult to keep the chip in superconducting state. With the positive feedback from a local hot spot under current bias, the chip rapidly heats up due to Joule heating. To increase the limit of power density, we propose an encapsulation method thatincreases the heat flux capacity of the system. With the encapsulation, the heat flux capacity of the system is increased to about 0.4 W/cm2.