A lot of people are interested in optical thermometry, especially the new single-band ratiometric (SBR) technology for measuring temperature. But since SBR thermometry is still in its infancy, it is highly constrained when compared to the conventional dual-band ratiometric approach. In this paper, we propose a new SBR thermometry technique that is based on both the ground and excited state absorption processes. When these two different processes occur, the green emission of Tb3+ in the low-cost host of NaSrGd(MoO4)3 (NSGM) responds to changes in temperature in a way that is the exact opposite of what you would expect. The maximum luminescence intensity was obtained for an optimum terbium concentration of 40% mol. The resulting chromaticity coordinates (x, y) and high correlated color temperature (CCT) values of the doped phosphors give a thermally stable cold emission in the green region with a color purity of about 92%. Using this intriguing characteristic as a foundation, sensitive SBR thermometry has been successfully developed, and the optical properties of the material have also been thoroughly researched. At room temperature, the relative sensitivity reaches its maximum value of 10.9% K-1. These findings may give important information that may be used in the design of new luminescent thermometers that have excellent performance.