  We present the ultra-low-temperature thermal conductivity measurements on
single crystals of the prototypical charge-density-wave material 1$T$-TaS$_2$,
which was recently argued to be a candidate for quantum spin liquid. Our
experiments show that the residual linear term of thermal conductivity at zero
field is essentially zero, within the experimental accuracy. Furthermore, the
thermal conductivity is found to be insensitive to the magnetic field up to 9
T. These results clearly demonstrate the absence of itinerant magnetic
excitations with fermionic statistics in bulk 1$T$-TaS$_2$ and, thus, put a
strong constraint on the theories of the ground state of this material.
