  The pseudopotential lattice Boltzmann (LB) model is a popular model in the LB
community for simulating multiphase flows. Recently, several thermal LB models,
which are based on the pseudopotential LB model and constructed within the
framework of the double-distribution-function LB method, were proposed to
simulate thermal multiphase flows [G. H\'azi and A. M\'arkus, Phys. Rev. E 77,
026305 (2008); L. Biferale et al., Phys. Rev. Lett. 108, 104502 (2012); S. Gong
and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)]. The objective of the
present paper is to show that the effect of the forcing term on the temperature
equation must be eliminated in the pseudopotential LB modeling of thermal
flows. First, the effect of the forcing term on the temperature equation is
shown via the Chapman-Enskog analysis. For comparison, alternative treatments
that are free from the forcing-term effect are provided. Subsequently,
numerical investigations are performed for two benchmark tests. The numerical
results clearly show that the existence of the forcing-term effect will lead to
significant numerical errors in the pseudopotential LB modeling of thermal
flows.
