The heat capacity C of two alloys of the composition ${\mathrm{Ni}}_{73.75}$${\mathrm{Al}}_{26.25}$ (alloy IV) and ${\mathrm{Ni}}_{76.41}$${\mathrm{Al}}_{23.59}$ (alloy V) has been measured in the temperature range 1.5--20 K. Magnetization as a function of temperature and applied magnetic field has also been studied for these two alloys and three other alloys (alloys I, II, and III: ${\mathrm{Ni}}_{74.75}$${\mathrm{Al}}_{25.25}$, ${\mathrm{Ni}}_{75.00}$${\mathrm{Al}}_{25.00}$, and ${\mathrm{Ni}}_{75.60}$${\mathrm{Al}}_{24.40}$, respectively) which had been studied calorimetrically earlier [Phys. Rev. B 39, 7453 (1989)]. The C/T versus ${T}^{2}$ plot of alloy V is linear in the range 1.5--12 K but a barely discernible upturn exists for alloy IV below about 6 K. From Arrott plots magnetic ordering temperatures of 38.2 and 68.9 K, and spontaneous moments of 0.076 and 0.114${\ensuremath{\mu}}_{B}$/Ni at 5 K were obtained for alloys III and V, respectively. Alloys I, II, and IV, however, are paramagnetic down to at least 5 K. The Curie temperatures of the ordered alloys III and V, when determined and compared with previous results published in the literature, show a composition shift between our chemically analyzed samples and those measured on nominal composition alloys. The difference is thought to be due to a loss of aluminum by vaporization during the sample preparation. These results, taken together with our earlier results, show that for some compositions the upturn in the C/T plots of well prepared ``${\mathrm{Ni}}_{3}$Al'' alloys, which have a solid solution range from 72.5 to 77 at. % Ni, is due to spin fluctuations and not due to magnetic clusters. Furthermore, our results show, for the first time, that the electronic specific-heat constant and the upturn approach a maximum as the composition approaches the spin-fluctuator--ferromagnetic crossover point (75.1 at. % Ni) from either side in accord with theory.