The common ice plant (Mesembryanthemum crystallinum L.) has some medicinal uses and recommended plant in closed-type plant factory. The objective of this study was to estimate the cardinal temperatures for seed germination of the common ice plant using bilinear, parabolic, and beta distribution models. Seeds of the common ice plant were germinated in the dark in a growth chamber at four constant temperatures: 16, 20, 24, and $28^{\circ}C$. For this, four replicates of 100 seeds were placed on two layers of filter paper in a 9-cm petri dish and radicle emergence of 0.1 mm was scored as germination. The times to 50% germination were 4.3, 2.5, 2.0, and 1.8 days at 16, 20, 24, and $28^{\circ}C$, respectively, indicating that the germination of this warm-weather crop increased with temperature. Next, the time course of germination was modeled using a logistic function. For the selection of an accurate model, seeds were germinated in the dark at constant temperatures of 6, 12, 32, and $36^{\circ}C$. Germination started earlier and increased rapidly at temperatures above $20^{\circ}C$. The minimum, optimal, and maximum temperatures were estimated by regression of the inverse of time to 50% germination rate, as a function of the temperature gradient. The different functions estimated differing minimum, optimal and maximum temperatures, with 5.7, 27.7, and $36.5^{\circ}C$, respectively for the bilinear function, 13.4, 25.0, and $36.6^{\circ}C$, respectively, for the parabolic function and 7.8, 25.9, and $36.0^{\circ}C$, respectively, for the beta distribution function. The models estimated that the inverse of time to 50% germination rate was 0 at 6 and $36^{\circ}C$. The observed final germination rates at 12 and $32^{\circ}C$ were 62 and 97%, respectively. Our data show that a beta distribution function provides a useful model for estimating the cardinal temperatures for germination of seed from the common ice plant.