Weakly nonlinear propagation of pressure waves in an initially quiescent compressible liquids uniformly containing many spherical microbubbles was theoretically studied by deriving the KdVB (Korteweg–de Vries–Burgers) equation. In particular, the energy equation at the bubble-liquid interface (Prosperetti, J. Fluid Mech., 222, 587, 1991) and the effective polytropic exponent were newly introduced into our model (Kanagawa et al., J. Fluid Sci. Technol., 6, 838, 2011) to clarify thermal effect inside the bubbles mainly on wave dissipation. Thermal conduction was investigated in detail by using some temperature-gradient models. The main results are summarized as follows: (i) Two types of dissipation term appeared: one was a well-known second-order derivative comprising the effect of viscosity and liquid compressibility (acoustic radiation), and the other was a newly discovered term without differentiation comprising the effect of thermal conduction. (ii) The thermal effect contributed to not only the dissipation effect but the nonlinear effect, and nonlinearity increased compared with that in Kanagawa et al. (2011). (iii) There were no significant differences among four temperature-gradient models for milliscale bubbles. However, thermal dissipation increased in four models for microscale bubbles. (iv) The thermal dissipation effect in this study was comparable with that in a KdVB equation derived by Prosperetti (1991) although the forms of dissipation terms describing the effect of thermal conduction differed.