We have observed a paramagnetic-to-ferromagnetic phase transition in short period InGaMnAs/InGaAs superlattices. The thicknesses of magnetic InGaMnAs layers in the structures studied was chosen to be 4 or 8 molecular layers (12 Å or 24 Å). The nonmagnetic InGaAs spacer layers are 12 Å thick. The In content of InGaMnAs and InGaAs layers was chosen in such a way that magnetic layers were: deep potential wells, high potential barriers or shallow potential wells. For superlattices with 8 monolayer thick InGaMnAs magnetic layers and 4 monolayer thick InGaAs nonmagnetic spacers the temperatures of paramagnetic-to-ferromagnetic phase transition do not depend on the band offsets between InGaMnAs and InGaAs adjusted by the In content.