Multi-messenger astronomy and time-domain astronomy are strongly linked even if they do not have the same objectives. Multi-messenger astronomy is an astrophysical observation approach born by the simultaneous, even if casual, detection of a few events discovered up to now. In contrast, time-domain astronomy is a recent technological trend that aims to make observations to explore the sky not with imaging, astrometry, photometry or spectroscopy but through the fast dynamic behavior of celestial objects. Time-domain astronomy aims to detect events on a temporal scale between seconds and nanoseconds. In this paper, a time-domain infrared fast detector for ground-based telescopes is proposed. This instrument can be useful for multi-messenger observations, and it is able to detect fast astronomical signals in the order of 1 ns. It is based on HgCdTe photoconductors, but the InAsSb photovoltaic detector has also been tested. The detection system designed to detect fast mid-infrared bursts includes trigger modules, an off-line noise-canceling strategy, and a classifier of the transients. Classification is derived from the analysis of fast instabilities in particle circular accelerators. This paper aims to be a preliminary feasibility study.