Neural networks are typically black-boxes that remain opaque with regards to their decision mechanisms. Several works in the literature have proposed post-hoc explanation methods to alleviate this issue. This paper proposes LMAC-TD, a post-hoc explanation method that trains a decoder to produce explanations directly in the time domain. This methodology builds upon the foundation of L-MAC, Listenable Maps for Audio Classifiers, a method that produces faithful and listenable explanations. We incorporate SepFormer, a popular transformer-based time-domain source separation architecture. We show through a user study that LMAC-TD significantly improves the audio quality of the produced explanations while not sacrificing from faithfulness.