  We consider the stochastic heat equation driven by a multiplicative Gaussian
noise that is white in time and spatially homogeneous in space. Assuming that
the spatial correlation function is given by a Riesz kernel of order $\alpha
\in (0,1)$, we prove a central limit theorem for power variations and other
related functionals of the solution. To our surprise, there is no asymptotic
bias despite the low regularity of the noise coefficient in the multiplicative
case. We trace this circumstance back to cancellation effects between error
terms arising naturally in second-order limit theorems for power variations.
