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• A transient temperature response analysis method based on the interval K-L expansion is proposed. • The time-variant uncertain parameters are quantified by an interval process model due to lack of sufficient sample data. • The analytical solution for the upper and lower bounds of the transient temperature responses are given. A transient temperature response analysis method for heat transfer problems with dynamic uncertain parameters is proposed. The time-variant or dynamic uncertain parameters are quantified by an interval process model using only the variation bounds of uncertainty, providing an effective way for problems where probabilistic modeling of the dynamic uncertainties is unfeasible due to lack of sufficient sample data. The interval Karhunen–Loève (K-L) expansion is adopted to represent the interval processes, thus describing accurately the continuous uncertainty over time by a series of interval variables. For convenience of solution, the Laplace transformation is then applied to transform the heat transfer uncertainty analysis over time domain to the complex field, where the analytical solution for the upper and lower bounds of the transient temperature responses can be obtained. Finally, the computational effectiveness and efficiency of the proposed method are verified by three typical numerical examples. [ABSTRACT FROM AUTHOR]