To improve the conservative estimate in traditional fuzzy reliability model, this paper proposes a new reliability analysis method for the fuzzy heat transfer system by using the novel interval ranking strategy. Fuzzy variables representing the subjective uncertainties in input parameters are transformed into a set of interval variables under different membership levels. By adopting the interval satisfaction degree to quantify the safety possibility and failure possibility, the proposed reliability model can efficiently utilize the uncertain information in the transition domain of limit state function, which is completely neglected in the traditional reliability model. Besides, as the basis of reliability analysis, a parameter perturbation method with small computational cost is presented for the fast prediction of uncertain temperature responses. By comparing results with traditional Monte Carlo simulation and fuzzy reliability model, two numerical examples evidence the feasibility and superiority of proposed method at fuzzy reliability analysis in practical engineering.