Localized thermoelectric "self cooling" in semiconductor materials is among the most promising approaches for the remediation of on-chip hot spots resulting from the shrinking feature sizes and faster switching speeds of nanoelectronic components. Self cooling in a germanium chip is investigated, using 3-dimensional, thermal-electric, coupled numerical simulations, for a range of systems and geometric parameters. The results suggest that localized cooling, associated with the introduction of an electric current on the back surface of a germanium chip, can effectively reduce the hot spot temperature rise on the active side of the chip. It was found that self cooling in a 100μm thick chip could provide between 3.9°C and 4.5°C hotspot temperature reduction. When using a germanium layer above an electrically insulated silicon layer, self-cooling was found to yield an additional 1°C to 2°C temperature reduction. A streamlined computational tool is developed to facilitate the identification of optimal cooling parameters.