  Electroweak symmetry non-restoration up to high temperatures well above the
electroweak scale offers new alternatives for baryogenesis. We propose a new
approach for electroweak symmetry non-restoration via an inert Higgs sector
that couples to the Standard Model Higgs as well as an extended scalar singlet
sector. We implement renormalization group improvements and thermal
resummation, necessary to evaluate the effective potential spanning over a
broad range of energy scales and temperatures. We present examples of benchmark
scenarios that allow for electroweak symmetry non-restoration all the way up to
hundreds of TeV temperatures, and also feature suppressed sphaleron washout
factors down to the electroweak scale. Our method for transmitting the Standard
Model broken electroweak symmetry to an inert Higgs sector has several
intriguing implications for (electroweak) baryogenesis, early universe thermal
histories, and can be scrutinized through Higgs physics phenomenology and
electroweak precision measurements at the HL-LHC.
