We studied segmented polyurethanes (SPU) from poly(diethylene glycol adipate) with molar masses M-SFT = 780, 1365, 1780 and 3200 g/mol (soft fragments, SFT), 2,4-toluene diisocyanaite and 2,4-toluene diamine (stiff fragments, STF) with essentially monodisperse molar mass distribution of STF. They were characterized by WAXS, SAXS, heat capacity measurements, mainly from 150-450 K, and enthalpies of solution in dimethyl formamide at room temperature, Delta H-sol. The experimental results may be summarized as follows. i). The glass transition temperatures of SFT decrease with an increase of M-SFT, but remain essentially composition-invariant at fixed M-SFT, whatever the STF volume fraction cp. ii). The surface-to-volume ratio of STF domains exhibits sudden, jump-like transitions at volume fractions phi* = 0.23 and phi** = 0.40, respectively. iii). Exothermic (i.e., negative) values of Delta H-sol exhibit a jump-like decrease at phi* = 0.23. It has been shown that the main cause of the latter effect is the transition of SFT from a somewhat extended to an essentially unperturbed conformation.