LiteBIRD is a JAXA-led international project that aims to test representative inflationary models by performing an all-sky cosmic microwave background radiation (CMB) polarization survey for 3 years at the Sun-Earth Lagrangian point L2. We aim to launch LiteBIRD in the late 2020s. The payload module (PLM) is mainly composed of the Low-Frequency Telescope (LFT), the Mid-Frequency Telescope and High-Frequency Telescope (MHFT), and a cryo-structure. To conduct the high-precision and high-sensitivity CMB observations, it is required to cool the telescopes down to less than 5 K and the detectors down to 100 mK. The high temperature stability is also an important design factor. It is essential to design and analyze the cryogenic thermal system for PLM. In this study, the heat balance, temperature distribution, and temperature stability of the PLM for the baseline design are evaluated by developing the transient thermal model. The effect of the Joule-Thomson (JT) coolers cold tip temperature variation, the periodical changes in subK Adiabatic Demagnetization Refrigerator (ADR) heat dissipation, and the satellite spin that generates the variable direction of solar flux incident are implemented in the model. The effect of contact thermal conductance in the LFT and the emissivity of the V-groove on the temperature distribution and heat balance are investigated. Based on the thermal analysis, it was confirmed that the PLM baseline design meets the requirement of the temperature and the cooling capability of the 4K-JT cooler. In addition, the temperatures of the V-groove and the LFT 5-K frame are sufficiently stable for the observation. The temperature stability of the Low Frequency Focal Plane (LF-FP) is also discussed in this paper.