The ternary intermetallic compound Gd$_2$Cu$_2$In crystallizes in Mo$_2$Fe$_2$B type structure with the space group $P4/mbm$ and we study critical behaviour and magnetocaloric effect near the ferromagnetic transition ($T_C$ $approx$ 94 K) using the magnetic and heat capacity measurements. The maximum entropy change ($Delta S_m$) and adiabatic temperature change ($Delta T_{ad}$) for the field value of 7 T were observed to be 13.8 J/kg.K and 6.5 K respectively. We have employed modified Arrott plot (MAP), Kouvel-Fisher (KF) procedures to estimate the critical exponents near the FM-PM phase transition. Critical exponents $beta$ = 0.312(2), $gamma$ = 1.080(5) are self-consistently estimated from the non-linear fitting. The $beta$ value is close to the three dimensional (3D) Ising model where as $gamma$ and $delta$ values are close to mean field model. The estimated critical exponents for Gd$_2$Cu$_2$In suggest that the system may belong to different universal class. All the three critical exponent obey Widom scale and collapse the scaled magnetic isotherms into two distinct branches below and above $T_C$ in accordance with single scaling equation. Specific heat measurements show a $lambda$ type peak near 94 K confirming the bulk magnetic ordering. The data near $T_C$ was fitted using the non-linear function $C_{P} = B + Cepsilon + A^{pm}|epsilon|^{-alpha}(1 + E^{pm} |epsilon|^{0.5})$ between -0.025$<epsilon<$0.025 which yielded the fourth critical exponent $alpha$ value to be 0.11 (3). The value indicates possible 3D-Ising behavior where Gd$^{3+}$ moments arranged uniaxially along long tetragonel axis c as reported in literature.
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