The interatomic exchange interactions and Curie temperatures in Ni-based full Heusler alloys Ni₂MnX with X=Ga,In,Sn, and Sb are studied within the framework of the density-functional theory. The calculation of the exchange parameters is based on the frozen-magnon approach. Despite closeness of the experimental Curie temperatures for all four systems, their magnetism appeared to differ strongly. This difference involves both the Mn-Mn and Mn-Ni exchange interactions. The Curie temperatures, T_C, are calculated within the mean-field approximation by solving a matrix equation for a multisublattice system. Good agreement with experiment for all four systems is obtained. The role of different exchange interactions in the formation of T_C of the systems is discussed.