Recent analyses of cosmological data suggest the presence of an extra relativistic component beyond the Standard Model content. The Higgs-Dilaton cosmological model predicts the existence of a massless particle - the dilaton - associated with the spontaneous symmetry breaking of scale invariance and undetectable by any accelerator experiment. Its ultrarelativistic character makes it a suitable candidate for contributing to the effective number of light degrees of freedom in the Universe. In this Letter we analyze the dilaton production at the (p)reheating stage right after inflation and conclude that no extra relativistic degrees of freedom beyond those already present in the Standard Model are expected within the simplest Higgs-Dilaton scenario. The elusive dilaton remains thus essentially undetectable by any particle physics experiment or cosmological observation. (C) 2012 Elsevier B.V. All rights reserved.