In this paper, we are interested in the rate of convergence for the central limit theorem of the maximum likelihood estimator of the drift coefficient for a stochastic partial differential equation based on continuous time observations of the Fourier coefficients u i (t) , i = 1 , ... , N of the solution, over some finite interval of time [ 0 , T ] . We provide explicit upper bounds for the Wasserstein distance for the rate of convergence when N → ∞ and/or T → ∞ . In the case when T is fixed and N → ∞ , the upper bounds obtained in our results are more efficient than those of the Kolmogorov distance given by the relevant papers of Mishra and Prakasa Rao, and Kim and Park. [ABSTRACT FROM AUTHOR]