This study was aimed at showing a procedure for calculating ranges of stress and strain fluctuations from a given wall temperature transient to assess the fatigue life at tee junctions where fluids of different temperatures flow in. The elastic and elastic-plastic structural analyses were performed for a mixing tee pipe made of stainless steel. The pipe wall temperature transient obtained by a mock-up test was used for the analyses. Bi-linear stress-strain curves were assumed for the elastic-plastic analysis. Results obtained by the elastic and elastic-plastic analyses were compared to investigate the influence of the plastic deformation on stress and strain fluctuations. It was shown that the stress and strain fluctuations were relatively large near the boundary of the hot spot, where relatively large compressive stress was caused by hot water that came from the branch pipe. The strain range obtained by the elastic-plastic analysis was almost the same as that obtained by the elastic analysis even if plastic strain was significant. It was concluded that, since the fatigue life was correlated not with the stress range but with the strain range, the fatigue life could be predicted using the strain range obtained by the elastic analysis without considering the plastic deformation. It was also pointed out that consideration of the effects of the mean stress and mean strain was not necessary in the fatigue damage assessment.