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Monte Carlo simulations have been carried out to study the effect of temperature on the growth kinetics of a circular grain. This work demonstrates the importance of roughening fluctuations on the growth dynamics. Since the effect of thermal fluctuations is stronger in d=2 than in d=3, as predicted by d=3 theories of domain kinetics, the circular domain shrinks linearly with time as A(t)=A(0)-αt, where A(0) and A(t) are the initial and instantaneous areas, respectively. However, in contrast to d=3, the slope α is strongly temperature dependent for T≥0.6T C . An ana lytical theory which considers the thermal fluctuations agrees with the T dependence of the Monte Carlo data in this regime, and this model show that these fluctua tions are responsible for the strong temperature de pendence of the growth rate for d =2. Our results are particularly relevant to the problem of domain growth in surface science.