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.
