  We study theories which naturally select a vacuum with parametrically small
Electroweak Scale due to finite temperature effects in the early universe. In
particular, there is a scalar with an approximate shift symmetry broken by a
technically natural small coupling to the Higgs, and a temperature dependent
potential. As the temperature of the universe drops, the scalar follows the
minimum of its potential altering the Higgs mass squared parameter. The scalar
also has a periodic potential with amplitude proportional to the Higgs
expectation value, which traps it in a vacuum with a small Electroweak Scale.
The required temperature dependence of the potential can occur through strong
coupling effects in a hidden sector that are suppressed at high temperatures.
Alternatively, it can be generated perturbatively from a one-loop thermal
potential. In both cases, for the scalar to be displaced, a hidden sector must
be reheated to temperatures significantly higher than the visible sector.
However this does not violate observational constraints provided the hidden
sector energy density is transferred to the visible sector without disrupting
big bang nucleosynthesis. We also study how the mechanism can be implemented
when the visible sector is completed to the Minimal Supersymmetric Standard
Model at a high scale. Models with a UV cutoff of 10 TeV and no fields taking
values over a range greater than 10^12 GeV are possible, although the scalar
must have a range of order 10^8 times the effective decay constant in the
periodic part of its potential.
