By exploiting the small bend radius achievable using high-index-contrast silicon photonic wire waveguides, we demonstrate a new low power thermo-optic switch arranged in a dense, double spiral geometry. Such a design permits the waveguide length to be extended for increased phase shift, without the need for increased heated volume. This provides an effective means to reduce the power consumption of thermo-optic switches, as well as a compact geometry desirable for the development of switch arrays. A low switching power of 6.5 mW was obtained for a spiral-path Mach-Zehnder interferometer device having a 10% - 90% rise time of 14 micros. The switching power is shown to be reduced by more than 5 times compared to a Mach-Zehnder interferometer employing a conventional straight waveguide geometry.