Accounting for longitudinal spin fluctuations in the paramagnetic state, we calculate elastic constants and stacking fault energy as a function of temperature and chemical composition for Cr-Co-Ni alloys. The longitudinal spin fluctuations are demonstrated to be important for the quantitative description of the thermo-mechanical properties and the corresponding chemical and temperature dependences. Replacing Ni with Cr and Co is found to yield opposite influence on the mechanical properties at finite temperature. A high thermal stability in plasticity is predicted in the low Cr regime in Cr-Co-Ni alloys, while a good thermal stability in elasticity can be achieved in the high Cr and low Co regime. The present advance in thermo-chemical-magnetic-property enhances the understanding required for an intelligent design of multicomponent alloys toward high-technology applications. Published under an exclusive license by AIP Publishing.