  We calculate the momentum distribution n(k) of the Unitary Fermi Gas using
Quantum Monte Carlo calculations at finite temperature T/\epsilon_F as well as
in the ground state. At large momenta k/k_F, we find that n(k) falls off as
C/k^4, in agreement with the Tan relations. From the asymptotics of n(k), we
determine the contact C as a function of T/\epsilon_F and present a comparison
with theory. At low T/\epsilon_F, we find that C increases with temperature,
and we tentatively identify a maximum around T/\epsilon_F \simeq 0.4. Our
calculations are performed on lattices of spatial extent up to N_x = 14 with a
particle number per unit volume of \simeq 0.03 - 0.07.
