Covert channels aim to hide the existence of communication. Recently, Murdoch proposed a temperature-based covert channel where information is transmitted by remotely inducing and measuring changes of temperature of an unwitting intermediate host. The channel was invented for the purpose of attacking anonymous servers, but could also be used for general-purpose covert communications. We propose an empirical method for estimating realistic (and previously unknown) capacities for this channel. In example scenarios with different intermediate hosts and different levels of temperature induction and noise we find the channel capacity is up to 20.5 bits per hour, but it almost halves to 10.3 bits per hour with higher noise or more effective cooling at the intermediate host.