Covert channels aim to hide the existence of communication between two or more parties. Such channels typically utilise pre-existing overt data transmissions to carry hidden messages. Recently, Murdoch proposed a temperature-based covert channel where information is transmitted by remotely inducing and measuring changes of temperature of an intermediate/target host. The channel was invented mainly for the purpose of attacking anonymous servers, but could also be used for general-purpose covert communications. We propose a method for estimating the channel capacity, which largely depends on the intermediate host. Evaluation of two different intermediate hosts shows upper bounds for the channel capacity of 10.8-15.4 and 16.4-21.1 bits per hour depending on the noise.