  We deal with parametric estimation for a parabolic linear second order
stochastic partial differential equation (SPDE) with a small dispersion
parameter based on high frequency data which are observed in time and space. By
using the thinned data with respect to space obtained from the high frequency
data, the minimum contrast estimators of two coefficient parameters of the SPDE
are proposed. With these estimators and the thinned data with respect to time
obtained from the high frequency data, we construct an approximation of the
coordinate process of the SPDE. Using the approximate coordinate process, we
obtain the adaptive estimator of a coefficient parameter of the SPDE. Moreover,
we give simulation results of the proposed estimators of the SPDE.
