To reduce the self-heating effect of strained Si grown on relaxed SiGe-on-insulator (SGOI) n-type metal-oxide-semiconductor field-effect transistors (nMOSFETs), this paper proposes a novel device called double step buried oxide (BOX) SGOI, investigates its electrical and thermal characteristics, and analyzes the effect of self-heating on its electrical parameters. During the simulation of the device, a low field mobility model for strained Si MOSFETs is established and reduced thermal conductivity resulting from phonon boundary scattering is considered. A comparative study of SGOI nMOSFETs with different BOX thicknesses under channel and different channel strains has been performed. By reducing moderately the BOX thickness under the channel, the channel temperature caused by the self-heating effect can be effectively reduced. Moreover, mobility degradation, off state current and a short-channel effect such as drain induced barrier lowering can be well suppressed. Therefore, SGOI MOSFETs with a thinner BOX under the channel can improve the overall performance and long-term reliability efficiently.