We study the effect of localized Joule heating on the mechanical properties of doubly clamped nanowires under tensile stress. Local heating results in systematic variation of the resonant frequency; these frequency changes result from thermal stresses that depend on temperature dependent thermal conductivity and expansion coefficient. The change in sign of the linear expansion coefficient of InAs is reflected in the resonant response of the system near a bath temperature of 20 K. Using finite element simulations to model the experimentally observed frequency shifts, we show that the thermal conductivity of a nanowire can be approximated in the 10-60 K temperature range by the empirical form $κ=b$T W/mK, where the value of $b$ for a nanowire was found to be $b=0.035$ W/mK$^2$, significantly lower than bulk values. Also, local heating allows us to independently vary the temperature of the nanowire relative to the clamping points pinned to the bath temperature. We suggest a loss mechanism (dissipation $∼10^{-4}-10^{-5}$) originating from the interfacial clamping losses between the metal and the semiconductor nanostructure.