Chaotic thermal convection for infinite Prandtl number fluids in large aspect-ratio boxes is investigated within the framework of multimode mean-field theory. Various types of filtering models in the spectral space are employed to eliminate the excess energy which is present when only a few modes are taken in time-dependent spectral method. For Rayleigh numbers slightly in excess of 105the flow is chaotic but is still sufficiently regular so that the lowest three modes dominate the energetics of the flow. The quality of the filtering used in describing the real solution is evaluated in terms of the differences in compactness (fractal dimension) between the filtered strange attractor and the actual one.