  We report a study of the low-temperature heat transport in the
quasi-one-dimensional S = 1/2 alternating antiferromagnetic-ferromagnetic chain
compound (CH_{3})_{2}NH_{2}CuCl_{3}. Both the temperature and magnetic-field
dependencies of thermal conductivity are very complicated, pointing to the
important role of spin excitations. It is found that magnetic excitations act
mainly as the phonon scatterers in a broad temperature region from 0.3 to 30 K.
In magnetic fields, the thermal conductivity show drastic changes, particularly
at the field-induced transitions from the low-field N\'{e}el state to the
spin-gapped state, the field-induced magnetic ordered state, and the spin
polarized state. In high fields, the phonon conductivity is significantly
enhanced because of the weakening of spin fluctuations.
