We report a calorimetric study of a series of mixtures of two twist-bend liquid crystal dimers, the 1'',7''-bis(4-cyanobiphenyl)-4'-yl heptane (CB7CB) and 1''-(2',4-difluorobiphenyl-4'-yloxy)-9''-(4-cyanobiphenyl-4'-yloxy) nonane (FFO9OCB), the molecules of which have different effective molecular curvatures. High-resolution heat capacity measurements in the vicinity of the NTB-N phase transition for a selected number of binary mixtures clearly indicate a first order NTB-N phase transition for all the investigated mixtures, the strength of which decreases when the nematic range increases. Published theories predict a second order NTB-N phase transition, but we have developed a self-consistent mean field Landau model using two key order parameters: A symmetric and traceless tensor for the orientational order and a short-range vector field which is orthogonal to the helix axis and rotates around of the heliconical structure with an extremely short periodicity. The theory, in its simplified form, depends on two effective elastic constants and explains satisfactorily our heat capacity measurements and also predicts a first-order NTB-N phase transition. In addition, as a complementary source of experimental measurements, the splay (K1) and bend (K3) elastic constants in the conventional nematic phase for the pure compounds and some selected mixtures have been determined.