Tunable diode laser absorption spectroscopy (TDLAS) tomography is a well-established combustion diagnostic technique for imaging two-dimensional cross-sectional distributions of critical flow-field parameters. As two key metrics in TDLAS tomography, reconstruction accuracy and efficiency are generally traded off to satisfy either the requirement of highfidelity image retrieval or rapid tomographic data inversion. In this paper, a novel quality-hierarchical temperature imaging network for TDLAS tomography is developed based on stacked Long Short Term Memory (LSTM). From limited line-of-sight TDLAS measurements, this network outputs two reconstructed temperature images, i.e. a coarse-quality image and a fine-quality image, with different numbers of network layers and consequently different computational costs. The coarse-quality image provides more timely temperature reconstruction, which can satisfy realtime dynamic monitoring of turbulence-chemistry interactions with a temporal resolution of tens of kilo frames per second. On the other hand, the fine-quality image, that can be stored and utilized for offline analysis and diagnosis, further details the temperature reconstruction with more accurate features. Both numerical stimulation and lab-scale experiment validated the accuracy-efficiency trade-off achieved by the proposed qualityhierarchical temperature imaging network.