Spatial conformations of a model polymerized membrane (tethered surface) with a quenched in-plane disorder have been studied using Monte Carlo methods. As the temperature decreases the membrane first undergoes a transition from a crumpled to fluctuating flat state. Specific heat singularity is detected at the transition point. Further decrease of the temperature freezes the transverse fluctuations, but does not cause the membrane to approach a flat state. On the contrary, the deviation from a flat configuration increases, and the membrane settles into a partially folded ground state.