Title: Low temperature specific heat and thermal conductivity in superconducting UTe2

Abstract: The measurements (Phys.Rev.B {\bf 100}, 220504(R) (2019)) do not detect noticeable thermal conductivity in superconducting UTe$_2$ in the T=0 limit. At the same time the same crystals exhibit a large residual density of states comparable with its normal state value. The improvement of samples quality leads to the augmentation of critical temperature of transition to the superconducting state accompanied by the decreasing of residual specific heat ratio $C(T)/T$ at $T\to 0$. There is presented an analytic derivation of this inverse correlation property in concrete cases of triplet superconducting states with node-less and point-nodes order parameters allowed by symmetry in UTe$_2$. The obtained explicit formulas for the residual thermal conductivity are in reasonable correspondence with observations.