The thermal conductivity of YbRh_{2}Si_{2} has been measured down to very low temperatures under field in the basal plane. An additional channel for heat transport appears below 30 mK, both in the antiferromagnetic and paramagnetic states, respectively, below and above the critical field suppressing the magnetic order. This excludes antiferromagnetic magnons as the origin of this additional contribution to thermal conductivity. Moreover, this low temperature contribution prevails a definite conclusion on the validity or violation of the Wiedemann-Franz law at the field-induced quantum critical point.