We report the boiling behaviour of pentane emulsified in a yield stress fluid, a colloidal clay (Laponite) suspension. We have observed that a superheated state is easily reached: the emulsion, heated more than 50°C above the alkane boiling point, does not boil. Superheating is made possible by the suppression of heterogeneous nucleation in pentane, resulting from the emulsification process, a phenomenon evidenced decades ago in studies of the superheating of two phase fluids. We have furthermore studied the growth of isolated bubbles nucleated in the emulsion. The rate of increase of the bubble radius with time depends on both the temperature and emulsion volume fraction but, rather unexpectedly, does not depend on the fluid rheology. We show that the bubbles grow by diffusion of the alkane through the aqueous phase, between liquid droplets and bubbles, analogously to an Ostwald ripening process. The peculiarity of the process reported here is that a layer depleted in oil droplets forms around the bubble, layer to which the alkane concentration gradient is confined. We successfully describe our experimental results with a simple transfer model.