Planets form in disks around young stars. The planet formation process may start when the protostar and disk are still deeply embedded within their infalling envelope. However, unlike more evolved protoplanetary disks, the physical and chemical structure of these young embedded disks are still poorly constrained. We have analyzed ALMA data for 13CO, C18O and N2D+ to constrain the temperature structure, one of the critical unknowns, in the disk around L1527. The spatial distribution of 13CO and C18O, together with the kinetic temperature derived from the optically thick 13CO emission and the non-detection of N2D+, suggest that this disk is warm enough (≳ 20 K) to prevent CO freeze-out.