  We present a comprehensive study of the frequency-dependent sensitivity for
measurements of the AC elastocaloric effect by applying both exactly soluble
models and numerical methods to the oscillating heat flow problem. These models
reproduce the finer details of the thermal transfer functions observed in
experiments, considering here representative data for single-crystal
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. Based on our results, we propose a set of
practical guidelines for experimentalists using this technique. This work
establishes a baseline against which the frequency response of the AC
elastocaloric technique can be compared and provides intuitive explanations of
the detailed structure observed in experiments.
