  We report the detailed analysis of temperature dependent neutron diffraction
pattern of the Cr$_2$CoAl inverse Heusler alloy and unveil the magnetic
structure up to the phase transition as well as its fully compensated
ferrimagnetic nature. The Rietveld refinement of the diffraction pattern using
the space group I$\bar4${\it m}2 confirm the inverse tetragonal structure over
the large temperature range from 100~K to 900~K. The refinement of the magnetic
phase considering the wave vector $k=$ (0, 0, 0) reveals the ferrimagnetic
nature of the sample below 730$\pm$5~K. This transition temperature is obtained
from empirical power law fitting of the variation in the ordered net magnetic
moment and intensity of (110) peak as a function of temperature. The spin
configuration of the microscopic magnetic structure suggests the nearly fully
compensated ferrimagnetic behavior where the magnetic moments of Cr2 are
antiparallel with respect to the Cr1, and Co moments. Moreover, the observed
anomaly in the thermal expansion and lattice parameters at 730$\pm$5~K suggest
that the distortion in crystal structure may play an important role in the
magnetic phase transition.
