The aim of this paper is to establish non-asymptotic minimax rates for goodness-of-fit hypotheses testing in an heteroscedastic setting. More precisely, we deal with sequences (Y_j)_j∈J of independent Gaussian random variables, having mean (θ_j)_j∈J and variance (σ_j)_j∈J. The set J will be either finite or countable. In particular, such a model covers the inverse problem setting where few results in test theory have been obtained. The rates of testing are obtained with respect to l₂ norm, without assumption on (σ_j)_j∈J and on several functions spaces. Our point of view is entirely non-asymptotic.