Therefore, in this study, based on energy balance principle between wellbore and formation, a temperature model of drilling fluid layers was established under different grid units of wellbore condition. Meanwhile, the axial thermal conductivity temperature model of drilling fluid was established by introducing axial conduction items of drilling fluid, followed by using discrete and solving of implicit finite difference method to these mathematical models. The calculation results indicated that the error temperature of the radial and axial of drilling fluid wellbore temperature which was caused of radial temperature gradient were 0.15 and 0.2 ◦C respectively, whereas axis thermal conductivity of drilling fluid has little effect on wellbore temperature distribution. Therefore, the above results confirmed that it can ignore both of them to influence wellbore temperature distribution by established the wellbore-formation coupled transient heat transfer model. Moreover, it is the first proved the correctness of model assumptions from previous scholars based on the mathematical modeling methods, and then further provides the reliable theoretical basis for down-hole temperature distribution of oil and gas well and geothermal well.% 本文基于井筒与地层间能量平衡原理，将井筒钻井液划分成不同径向单元网格，建立了考虑径向温度梯度条件下钻井液层间温度模型；同时引入钻井液轴向导热项，建立了钻井液轴向导热温度模型，将数学模型应用隐式有限差分法离散与求解.计算结果表明：钻井液径向温度梯度对井筒径向与轴向温度产生的误差分别为0.15◦C和0.2◦C左右；而钻井液轴向导热对井筒温度分布几乎不产生影响.因此，通过建立的数学模型进行系统分析表明，在建立井筒-地层耦合瞬态传热模型时可忽略两者对井筒温度分布的影响.基于数学建模方法验证了以前学者模型假设条件的正确性，为油气井与地热井井下温度分布规律深入研究奠定了可靠的理论基础.
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