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Small concentrations of alloying elements can modify the <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-<inline-formula> <math display="inline"> <semantics> <mi>&#947;</mi> </semantics> </math> </inline-formula> phase transition temperature <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> of Fe. We study this effect using an atomistic model based on a set of many-body interaction potentials for iron and several alloying elements. Free-energy calculations based on perturbation theory allow us to determine the change in <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>c</mi> </msub> </semantics> </math> </inline-formula> introduced by the alloying element. The resulting changes are in semi-quantitative agreement with experiment. The effect is traced back to the shape of the pair potential describing the interaction between the Fe and the alloying atom.