Precision cosmology provides a sensitive probe of extremely weakly coupled states due to thermal freeze-in production, with subsequent decays impacting physics during well-tested cosmological epochs. We explore the cosmological implications of the freeze-in production of a new scalar S via the superrenormalizable Higgs portal. If the mass of S is at or below the electroweak scale, peak freeze-in production occurs during the electroweak epoch. We improve the calculation of the freeze-in abundance by including all relevant QCD and electroweak production channels. The resulting abundance and subsequent decay of S is constrained by a combination of x-ray data, cosmic microwave background anisotropies and spectral distortions, Neff, and the consistency of big bang nucleosynthesis with observations. These probes constrain technically natural couplings for such scalars from mS∼10 keV all the way to mS∼100 GeV. The ensuing constraints are similar in spirit to typical beam dump limits, but extend to much smaller couplings, down to mixing angles as small as θSh∼10-16, and to masses all the way to the electroweak scale.