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A theoretical model capable of calculating transient temperature distribution and simulating the dynamic lasing behavior of a sampled grating distributed Bragg reflector (SG-DBR) tunable laser with the influence of thermal effects into account is described in this paper. Transient 3-D temperature distribution of an SG-DBR laser is modeled by numerically solving heat transfer equations using finite element method. Then, a temperature-dependent dynamic transfer matrix method based model of the laser is developed, which can take thermal effects into account. In this paper, we pay special attention to thermally induced wavelength drift and spectrum evolution under different combinations of tuning currents. Simulated results show that the wavelength drifts are usually in the order of several tens of picometers. Furthermore, when the tuning currents are switched to some certain values, thermal transients may cause mode hop or dual modes lasing. In these cases, total wavelength change induced by thermal effects can be as large as 0.6 nm.