Three-dimensional interconnected nickel–cobalt layered double hydroxides (NiCo-LDHs) were prepared on nickel foam by ion exchange using a cobalt-based metal–organic framework (Co-MOF) as a template at different temperatures. The effects of the Co-MOF preparation temperature on the growth, mass, morphology, and electrochemical properties of the Co-MOF and derived NiCo-LDH samples were studied. The synthesis temperature from 30 to 50 °C gradually increased the mass of the active material and the thickness of the Co-MOF sheets grown on the nickel foam. The higher the temperature is, the larger the proportion of Co3+. β-Cobalt hydroxide (β-Co(OH)2) sheets were generated above 60 °C. The morphology and mass loading pattern of the derived flocculent layer clusters of NiCo-LDH were inherited from metal-organic frameworks (MOFs). The areal capacitance of NiCo-LDH shows an inverted U-shaped curve trend with increasing temperature. The electrode material synthesized at 50 °C had a tremendous specific capacitance of 7631 mF·cm−2 at a current density of 2 mA·cm−2. The asymmetric supercapacitor assembled with the sample and active carbon (AC) achieved an energy density of 55.0 Wh·kg−1 at a power density of 800.0 W·kg−1, demonstrating the great potential of the NiCo-LDH material for energy storage. This work presents a new strategy for designing and fabricating advanced green supercapacitor materials with large power and energy densities.