  We report the structural, magnetic, and magnetocaloric properties of
Co$_2$Cr$_{1-x}$Ti$_x$Al ($x=$ 0--0.5) Heusler alloys for spintronic and
magnetic refrigerator applications. Room temperature X-ray diffraction and
neutron diffraction patterns along with Rietveld refinements confirm that the
samples are of single phase and possess a cubic structure. Interestingly,
magnetic susceptibly measurements indicate a second order phase transition from
paramagnetic to ferromagnetic where the Curie temperature (T$_{\rm C}$) of
Co$_2$CrAl increases from 330~K to 445~K with Ti substitution. Neutron powder
diffraction data of the $x=$ 0 sample across the magnetic phase transition
taken in a large temperature range confirm the structural stability and exclude
the possibility of antiferromagnetic ordering. The saturation magnetization of
the $x=$ 0 sample is found to be 8000~emu/mol (1.45~$\mu_{\rm B}$/{\it f.u.})
at 5~K, which is in good agreement with the value (1.35$\pm$0.05~$\mu_{\rm
B}$/{\it f.u.}) obtained from the Rietveld analysis of the neutron powder
diffraction pattern measured at temperature of 4~K. By analysing the
temperature dependence of the neutron data of the $x=$ 0 sample, we find that
the change in the intensity of the most intense Bragg peak (220) is consistent
with the magnetization behavior with temperature. Furthermore, an enhancement
of change in the magnetic entropy and relative cooling power values has been
observed for the $x=$ 0.25 sample. Interestingly, the critical behavior
analysis across the second order magnetic phase transition and extracted
exponents ($\beta\approx$ 0.496, $\gamma\approx$ 1.348, and $\delta\approx$
3.71 for the $x=$ 0.25 sample) suggest the presence of long-range ordering,
which deviates towards 3D Heisenberg type interactions above T$_{\rm C}$,
consistent with the interaction range value $\sigma$.
