In order to study the thermal safety of cylindrical battery deeply, based on the theory of heat transfer, thermal explosion and nonlinear modeling, a three-dimensional non-steady state thermal explosion mathematical model of cylindrical fireworks with non-uniform heat dissipation of the lateral surface was established for the first time (three-dimensional partial differential equation group). Combining seven point difference method and Newton-homotopy algorithm, the numerical calculation method of the three-dimensional non-steady state thermal explosion partial differential equation was established and the numerical calculation program was written base on Matlab. The validity of calculation program has been demonstrated by comparison of numerical solutions and classical solutions. The accuracy of model has been validated by example computation and analysis. The critical parameters describing non-steady state model of cylindrical fireworks when stored individually and stored in combination form were calculated in this paper, including temperature distribution, temperature-time history, thermal explosion time to ignition, etc. The results show that when the ambient temperature is 450 K, the fireworks stored individually do not have thermal explosion, but the fireworks stored in combination form will explode finally and the thermal explosion time to ignition is 19013.53 s. When the ambient temperature is 460 K, thermal explosion will occur in both the fireworks stored individually and stored in combination form, and the thermal explosion time to ignition are 3187.07 s and 3066.60 s respectively. It shows a more exact analytical methods and solutions of thermal safety evaluation of fireworks was established in this paper. Thus, it is need to strengthen the safety monitoring and management of cylindrical battery (combined fireworks) because of the higher thermal hazard. (C) 2016 Elsevier Ltd. All rights reserved.