Research on thermal response of liquid helium storage tank is an important part of non-destructive storage technology for liquid helium, However there are few reports on the thermal response of liquid helium storage tanks. Taking the thermal stratification, pressure rise phenomenon and natural convection of liquid helium storage tank as research objects, based on the Lee model, the finite volume method was used for the first time to study the non-steady-state thermal response which simultaneously considering the change of liquid helium and vapor helium properties. Thus the tank pressure, temperature and flow rate distribution at different times were obtained, and the effects of evaporation rate and filling rate on the pressure rise and temperature rise of the storage tank were analyzed. The research shows that with the increase of simulation time, the liquid helium shows thermal stratification. In addition, the pressure is distributed in a stepwise manner which is lower in the upper part, and higher in the lower part, while the pressure distribution in the gas phase space is more uniform; After the liquid helium in the near-wall area is heated, it rises along the wall surface to the free liquid surface under buoyancy lift, and then flows into the main flow area of the liquid helium; As the evaporation rate increases, the temperature rise and pressure rise rate in the gas phase space of the storage tank increase, while the filling rate have less influence on the temperature rise and pressure rise rate.This work provides guidance for non-destructive storage and transportation theory of liquid helium storage tanks.