Electrical-resistivity measurements at temperatures between 1.2 and 300 K and pressures up to 12 kbar have been used to determine that the pressure dependence of the Curie temperature ${\mathit{T}}_{\mathit{C}}$ of the ferromagnetic Heusler alloy ${\mathrm{Co}}_{2}$TiAl is -0.7 K/kbar. Analysis of the pressure dependence of ${\mathit{T}}_{\mathit{C}}$ in the Stoner-Wohlfarth theory of weak itinerant ferromagnetism reveals the important role of spin fluctuations in this material. Strong ferromagnetic ordering exists only in a limited range of nearest-neighbor cobalt-cobalt spacing in itinerant ferromagnets whose only potentially magnetic species is Co. Observation of the lack of correlation between Curie temperature and intermoment cobalt spacing is combined with the results of high-pressure measurements to identify cobalt Heusler alloys as examples of weak itinerant ferromagnets in which spin fluctuations are generically expected to make a significant contribution.