We present the ultralow-temperature specific heat and thermal conductivity measurements on single crystals of triangular-lattice organic compound EtMe$_3$Sb[Pd(dmit)$_2$]$_2$, which has long been considered as a gapless quantum spin liquid candidate. In specific heat measurements, a finite linear term is observed, consistent with the previous work [S. Yamashita $et$ $al.$, Nat. Commun. {bf 2}, 275 (2011)]. However, we do not observe a finite residual linear term in the thermal conductivity measurements, and the thermal conductivity does not change in a magnetic field of 6 Tesla. These results are in sharp contrast to previous thermal conductivity measurements on EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ [M. Yamashita $et$ $al.$ Science {bf 328}, 1246 (2010)], in which a huge residual linear term was observed and attributed to highly mobile gapless excitations, likely the spinons of a quantum spin liquid. In this context, the true ground state of EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ has to be reconsidered.
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