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The magnetic and magnetocaloric properties of Ni-Co-Mn-(Ga, In, Sn) Heusler intermetallics are discussed on the basis of ab initio and Monte Carlo calculations. The main emphasis is on the different reference spin states and magnetic exchange coupling constants of high-temperature austenite and low-temperature martensite which are very important for the calculation of magnetocaloric effect. The origin of metamagnetic behavior is considered in the framework of orbital resolved magnetic exchange parameters of austenite and martensite. The decomposition of exchange constants on orbital contributions has shown that a strong ferromagnetic interaction of magnetic moments in austenite is caused by the more itinerant d-electrons with t_2g states while a strong antiferromagnetic interaction in martensite is associated with the more localized eg states. In addition, the appearance of a paramagnetic gap between magnetically weak martensite and ferromagnetically ordered austenite can be realized because of strong competition of magnetic exchange interactions. As a result, large magnetization drop and giant inverse magnetocaloric effect can be achieved across the magnetostructural phase transition.