We derive arbitrage-free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein-Uhlenbeck process. Using a fractional white noise calculus, we can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and we show that these pricing formulas are solutions of certain Black & Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos (Quant. Finance, 2002).