  The radio frequency spectrum of the fermions in the unitary limit at finite
temperatures is characterized by the sum rule relations. We consider a simple
picture where the atoms are removed by radio frequency excitations from the
strongly interacting states into a state of negligible interaction. We
calculate the moments of the response function in the range of temperature
$0.08 \epsilon_F < T < 0.8 \epsilon_F$ using auxiliary field Monte Carlo
technique (AFMC) in which continuum auxiliary fields with a density dependent
shift are used. We estimate the effects of superfluid pairing from the clock
shift. We find a qualitative agreement with the pairing gap - pseudogap
transition behavior. We also find within the quasiparticle picture that in
order for the gap to come into quantitative agreement with the previously known
value at T=0, the effective mass has to be $m^* \sim 1.43 m$. Finally, we
discuss implications for the adiabatic sweep of the resonant magnetic field.
