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Suppose a terrestrial planet with no atmosphere is tidally locked and very near the star like a hot Jupiter.

Is the far side still very cold or would crust would conduct heat from the near side to far side?

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    $\begingroup$ The night side will be cold - Mercury is a good example as it has a very long "day". Have a look at this document as an example. $\endgroup$
    – Andy
    Aug 1, 2016 at 6:51

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The transfer of heat would be insignificant. Consider the Earth, the core is as hot as the surface of the sun. Some of this heat does get transferred to the surface, but it is only 0.03% of the energy received from the sun. Rock is a good insulator, most of the heat is transferred by convection.

The far side of a tidally locked planet would be very cold. It would receive very little heating from the planet's interior or the near side.

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