We propose and demonstrate an integrated wavemeter capable of accurate and broadband measurements without control or knowledge of the temperature. In our design, interferometers composed of silicon and silicon nitride waveguides enable accurate measurements of an input optical wavelength despite large and rapid temperature fluctuations of 20°C by leveraging the disparity in thermo-optic properties of the waveguides. We derive formulas which resolve the wavelength and temperature ambiguity of the interferometers. The fabricated wavemeter chip is found to have a mean accuracy of 11 pm over an 80 nm range near 1550 nm. To our knowledge, this is the first demonstration of an athermal silicon wavemeter and the lowest measurement error across such a broad wavelength range using silicon photonics. This result may reduce the cost and size of wavemeters used in combination with integrated lasers for optical communications, sensing, and other applications.