We have measured the low-temperature specific heat of the geometrically frustrated pyrochlore Heisenberg antiferromagnet Gd2Sn2O7 in zero magnetic field. The specific heat is found to drop exponentially below approximately 350 mK. This provides evidence for a gapped spin-wave spectrum due to an anisotropy resulting from single-ion effects and long-range dipolar interactions. The data are well fitted by linear spin-wave theory, ruling out unconventional low-energy magnetic excitations in this system, and allowing a determination of the pertinent exchange interactions in this material.