This study investigated the temperature dependence of the Young’s modulus and the thermal expansion of Fe–26 at%Mn base alloys. The addition of a few % of Ti, Mo, Nb, Zr, Ta, or Hf to the alloys limited the temperature coefficient of Young’s modulus to within ±5 × 10−5/K. In alloys with added Nb, Zr, and Hf, the temperature coefficient of thermal expansion was 1 × 10−5/K or less, whereas the Néel temperature was 380 K or greater. Fe–Mn-based alloys containing a few at% of elements from families 4 and 5 of the periodic table exhibited both Elinvar and Inver characteristics at temperatures up to approximately 380 K. The effect on the properties was shown to be correlated with the number of electrons in the outer shell of the added element and its atomic radius.