The gas kinetic temperature (TK) determines the physical and chemical evolution of the interstellar medium (ISM). However, obtaining reliable TK estimates usually requires expensive observations including the combination of multi-line analysis and dedicated radiative transfer calculations. This work explores the use of HCN and HNC observations, and particularly the I(HCN)-to-I(HNC) intensity ratio (I(HCN)/I(HNC)) of their J=1-0 lines, as direct probe of the gas kinetic temperature in the molecular ISM. We obtained a new set of large-scale observations of the HCN and HNC (1-0) lines throughout the Integral Shape Filament (ISF) in Orion. In combination with ancillary gas and dust temperature measurements, we find a systematic temperature dependence of the observed I(HCN)-to-I(HNC) intensity ratio throughout our maps. Additional comparisons with chemical models demonstrate that these observed I(HCN)/I(HNC) variations are driven by the effective destruction and isomerization mechanisms of HNC under low-energy barriers. The observed variations of I(HCN)/I(HNC) with TK can be described with a two-part linear function. This empirical calibration is then used to create a temperature map of the entire ISF. Comparisons with similar dust temperature measurements in this cloud, as well as in other regions and galactic surveys, validate this simple technique for obtaining direct estimates of the gas kinetic temperature in a wide range of physical conditions and scales with an optimal working range between 15K<TK<=40K. Both observations and models demonstrate the strong sensitivity of the I(HCN)/I(HNC) ratio to the gas kinetic temperature. Since these lines are easily obtained in observations of local and extragalactic sources, our results highlight the potential use of this observable as new chemical thermometer for the ISM.