The multi-segment liquid laser system connected in series and obliquely pumped by LD can have significantly improved laser beam quality and higher output power. A flow-heat-solid interaction model for calculating the temperature distribution in the sub-gain section is established, which is focused on the flow, heat transfer and coupling in sub-gain section. We performed the numerical simulation of transient flow-field-heat distribution by way of the finite element method. The method proposed precludes the influence of the inaccurate film coefficient on the calculation results, the film coefficient is no longer a prerequisite, but a result of the calculation. Our method provides a new effective way to assess and control the flow-field-heat distribution which is affected by the flow channel shape, flow rate, absorption coefficient and other factors. Numerical results show that the film coefficient is a function of spatial location. Flow and heat transfer effieciency decreases with increasing velocity. When the laser medium is flowing, the temperature distribution and temperature gradient distribution are similar and are complementary to the film coefficient distribution, the maximum temperature and temperature gradient appears in the sharp corner downstream the flow.