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Most cosmological models predict that the universe was hot and dense at theearly stages of it's evolution. In this paper we analyse the influence of thethermal bath of Standard Model particles on the dynamics of cosmological Higgsdomain walls. This manuscript poses an~extension of our earlier work in whichwe investigated the evolution of networks of Higgs domain walls neglecting theimpact of temperature variation.  Using the thermally corrected effective potential of Standard Model we havefound that both the position of the local maximum $h_{max}$ separating minimaand the width of domain walls strongly depend on temperature $T$. Fortemperatures higher than $10^{10}\; \textrm{GeV}$ they respectively increaseproportionally and decrease inverse proportionally to the increasingtemperature. Thus, the energy scale of the problem follows the value oftemperature.  Our numerical lattice simulations based on the PRS algorithm reveal thatHiggs domain walls in the presence of the background thermal bath are highlyunstable and decay shortly after formation. Moreover we have found that thefraction of horizons produced by inflation in which Higgs field expectationvalue is higher then $h_{max}$ needs to be very low in order for the evolutionof the~network of the domain walls to end in the electroweak vacuum. This meansthat Higgs domain walls necessarily were very rare objects and their averageenergy density was very small. As a result, the domain walls can notsignificantly effect cosmological observables.

Higgs domain walls in the thermal background