  The heat transport of the spin-gapped material (CH_3)_2CHNH_3CuCl_3
(IPA-CuCl_3), a candidate quantum magnet with Bose-Einstein condensation (BEC),
is studied at ultra-low temperatures and in high magnetic fields. Due to the
presence of the spin gap, the zero-field thermal conductivity (\kappa) is
purely phononic and shows a ballistic behavior at T < 1 K. When the gap is
closed by magnetic field at H = H_{c1}, where a long-range antiferromanetic
(AF) order of Cu^{2+} moments is developed, the magnons contribute
significantly to heat transport and exhibit a ballistic T^3 behavior at T < 600
mK. In addition, the low-T \kappa(H) isotherms show sharp peaks at H_{c1},
which indicates a gap re-opening in the AF state (H > H_{c1}) and demonstrates
limited applicability of the BEC model to IPA-CuCl_3.
