The linear theory of electrostatic instabilities driven by ion temperature gradient is investigated for impure plasmas in shaped (e.g., elliptical and triangular) toroidal plasma cross-sections. Kinetic theory is used to describe the response of each ion species. Both even and odd parity branches of these "lTG" modes are examined in detail for parameters relevant to high temperature experiments. The Shafranov shift tends to lower the growth rates of both nodes, most notably that of the odd parity mode. Ellipticity in the plasma cross section has a strong stabilizing effect on the even parity mode, but leaves the odd parity mode essentially unaffected. Triangularity has a much weaker (also stabilizing) effect and can be ignored, for practical situations. Strong stabilization by multiply charged impurities is encountered, primarily due to dilution of the primary ion concentration.