Infrared thermography (IRT) is increasingly deployed in noncontact condition monitoring, and further facilitates the machinery remaining useful life (RUL) prediction. For IRT-based prognostics, the interpretability of degradation features, the spatiotemporal denoising capability, and the effectiveness of uncertainty quantification are crucial issues. Therefore, this paper proposes an ensemble of deep spatiotemporal denoising wavelet networks (EDSDWN). Firstly, a 4D wavelet convolution layer (WCL) is designed to capture crucial degradation-related features with meaningful physical interpretability based on multi-resolution analysis. Secondly, noises existent in features are further filtered out in a restoration process by a proposed deep image stream denoiser (DISD) block with residual learning. A base DSDWN consisting of the WCL, the DISD, and a regressor is comprehensively constructed. Ultimately, the effective uncertainty quantification is implemented by EDSDWN adaptively fitting a RUL density with a Student-t mixture distribution. EDSDWN is constructed by employing an automatically weighted algorithm to incorporate multiple base DSDWNs. Experimental results on a thermal image dataset acquired from rotating machinery and a simulated dataset have proven that EDSDWN is tailored to IRT-based machine prognostics. This proposed method implements considerably lower prediction errors and higher effectiveness of uncertainty quantification than several advanced prognostics models.