Under the best atmospheric conditions mountain based telescopes have the potential to realize images with 0.25 arc second resolution. However, close thermal control of the observatory is needed to prevent local seeing from spoiling this quality. In particular it is very desirable to control the primary mirror surface temperature by removing heat from behind. In this paper we obtain expressions for the temperature of simple solid and honeycomb mirrors under a realistic observatory thermal environment and with different rates of heat removal. Heat transfer within a honeycomb structure by ventilation with air at ambient temperature is characterized by an efficiency and the mass transfer rate. Experimental values for efficiency are presented for a simple flow geometry. It is shown that readily achievable flow rates can produce the required thermal equilibrium of an 8m honeycomb mirror.