  We consider a special family of Gaussian hypergeometric functions whose
entries are cubic and trivial characters over finite fields. The special values
of these functions are known to give the Frobenius traces of families of
Hessian elliptic curves. Using the theory of harmonic Maass forms and mock
modular forms, we prove that the limiting distribution of these values is
semi-circular (i.e. $SU(2)$), confirming the usual Sato-Tate distribution in
this setting.
