  The holographic entanglement of purification (EoP) in AdS$_{4}$ and AdS-RN
black hole backgrounds is studied. We develop an algorithm to compute the EoP
for bipartite configuration with infinitely long strips. The temperature
behavior of EoP is revealed for small, intermediate and large configurations:
EoP monotonically increases with the temperature for small configurations;
while for intermediate configurations, EoP is configuration-dependent; EoP
vanishes for large configurations. Our numerical results verify some important
inequalities of EoP, which we also prove geometrically in Poincar\'e
coordinate.
