We present the results of a thorough study of the specific heat and magnetocaloric properties of a ludwigite crystal Cu2MnBO5 over a temperature range of 60 - 350 K and in magnetic fields up to 18 kOe. It is found that at temperatures below the Curie temperature (92 K), capacity possesses a linear temperature-dependent behavior, which is associated with the predominance of two-dimensional antiferromagnetic interactions of magnons. The temperature independence of capacity is observed in the temperature range of 95 - 160 K, which can be attributed to the excitation of the Wigner glass phase. The magnetocaloric effect (i.e. the adiabatic temperature change) was assessed through a direct measurement or an indirect method using the capacity data. Owing to its strong magnetocrystalline anisotropy, an anisotropic MCE or the rotating MCE is observed in Cu2MnBO5. A deep minimum in the rotating MCE near the TC is observed and may be associated with the anisotropy of the paramagnetic susceptibility.