We study the mechanical properties of ternary lipid bilayers assembled in giant vesicles, formed from a saturated and an unsaturated phosphocholine (in equal proportions) and cholesterol. As a function of temperature, these systems can undergo in-plane phase separation. Using image analysis we identify the vesicle contour, and quantify the vesicle shape and the amplitude of membrane thermal fluctuations. The two lipid compositions chosen show different thermotropic behaviours. At 60 mol% cholesterol the membrane is in a uniform liquid state over the entire temperature range investigated (10-50 °C), but vesicles containing 30 mol% cholesterol undergo phase separation into two immiscible liquid phases at around 28 °C. Upon cooling below this transition temperature we observe a marked increase in the measured bending elastic modulus. Phase separation proceeds over a long time (tens of minutes), and we measure the properties of vesicles both during the domain coarsening phase and in the fully phase separated condition. Fluorescence microscopy allows us to identify the coexisting phases. We can therefore measure directly the bending moduli of each of the phases as a function of temperature, showing a strong variation which is attributed to the changing phospholipid and cholesterol composition.