Recent theoretical work [H. Wu et al., Phys. Rev. Lett. 92, 237202 (2004); M. Hortamani et al., Phys. Rev. B 74, 205305 (2006); M. Hortamani, Ph.D. thesis, Freie Universität, Berlin, 2006] predicted ferromagnetism at zero temperature in thin MnSi films of B2-type crystal structure on Si(100). The relevance of this finding for finite-temperature experiments needs to be clarified by further investigations, since bulk MnSi is a weak ferromagnet with an experimentally measured Curie temperature of only T_C=30 K, and T_C is generally expected to be lower in thin films than in bulk materials. Here, we estimate T_C of such MnSi films using a multiple-sublattice Heisenberg model with first- and second-nearest-neighbor interactions determined from density functional theory calculations for various collinear spin configurations. The Curie temperature is calculated either in the mean-field approximation (MFA) or in the random-phase approximation (RPA). In the latter case we find a weak logarithmic dependence of T_C on the magnetic anisotropy parameter, which was calculated to be 0.4 meV for this system. In stark contrast to the above mentioned rule, large Curie temperatures of above 200 K for a monolayer (ML) MnSi film and above 300 K for a two ML MnSi film with B2-type structure on Si(100) are obtained within the RPA, and even higher values in MFA. Complementary calculations of MnSi bulk structures and thin unsupported MnSi films are performed in order to analyze these findings. We find that bulk MnSi in the cubic B2 structure is paramagnetic, in contrast to MnSi in the B20 ground-state structure in agreement with the Stoner criterion. In a tetragonally distorted B2 structure, the Mn atoms gradually develop a spin magnetic moment, passing through a low-spin and a high-spin state. However, the ferromagnetism of the MnSi/Si(100) films cannot be explained by tetragonal distortions alone, since the distorted B2 bulk structure is found to order antiferromagnetically. Comparison of the calculations of supported and unsupported films suggests that the reduced coordination of Mn atoms near surfaces and interfaces is crucial for the ferromagnetic ground state of the films. The coordination number of the Mn atoms in B2-type MnSi films on Si(100) constitutes a borderline case, where the spin magnetic moments of Mn are still large despite their sixfold coordination to Si, but the sp-d hybridization with Si states gives rise to a sizable ferromagnetic coupling of the Mn spins. We conclude that the Curie temperatures predicted from the Heisenberg Hamiltonian make thin MnSi films an interesting subject for further experimental investigation of spintronics materials.