In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x)){\rm d}t+ \sum_{k=1}^{\infty} g^{k}(t,x) \delta \beta_t^k, t \in [0,T]$, with random coefficients f and gk,
driven by a sequence (βk)k of i.i.d. fractional Brownian
motions of index H>1/2. Using the Malliavin calculus techniques
and a p-th moment maximal inequality for the infinite sum of
Skorohod integrals with respect to (βk)k, we prove that the
equation has a unique solution (in a Banach space of summability
exponent p ≥ 2), and this solution is Hölder continuous in
both time and space.