We analyse a possible adjustment of Twin Higgs models allowing to have broken electroweak (EW) symmetry at all temperatures below the sigma-model scale ∼ 1 TeV. The modification consists of increasing the Yukawa couplings of the twins of light SM fermions. The naturalness considerations then imply a presence of relatively light electroweak-charged fermions, which can be produced at the LHC, and decay into SM gauge and Higgs bosons and missing energy. Analysis of experimental bounds shows that such a modified model features an increased amount of fine-tuning compared to the original Twin Higgs models, but still less tuning than the usual pseudo-Nambu-Goldstone Higgs models not improved by Z2 twin symmetry. The obtained modification in the evolution of the EW symmetry breaking strength can, in particular, have interesting implications for models of EW baryogenesis, which we comment on.