Spacecraft external heat flux is very important for researching deterioration law of thermal control coating on orbit,influence of various spatial factors on thermal control products,as well as plume thermal effect of spacecraft attitude and orbit control engine. However,there are many difficulties in direct heat flux measurement. Thus,the inverse heat conduction problem can be used to get results which can satisfy certain precision. Firstly,in order to deduce transient external heat flux of spacecraft on orbit from telemetry temperature of spacecraft equipment on orbit,inverse heat conduction problem mathematical model was set up and solved by the conjugate gradient method. Iterative process of conjugate gradient method was improved according to physics concept in order to increase its anti instabilit. Then,two numerical tests were used for the purpose of checking mathematical model effect. The numerical tests could represent external heat flux change of most both earth-orbiting spacecraft and deep space exploration spacecraft. The maximum relative deviation between inversion value and true value is 2. 9% except step change data. Inversion results of the mathematical model is very good. Furthermore,satisfied results can be obtained by processing data analysis for absorbed external heat flux at step change location.