The Ni1−xCuxS2 pyrite (x≤0.07) is a model material where the impact of electron filling on a half-filled eg band system can be separated from changes in the bandwidth, since the unit cell volume does not change with x. This contrasts with the NiS2−xSex system where the size difference between S2− and Se2− makes the bandwidth vary at constant band filling. Our magnetic measurements show that there exists a clear relation between the presence of the antiferromagnetic phase developing below TN2=29.75K and charge localization. With the addition of Cu in Ni1−xCuxS2, the ground state evolves towards a metallic paramagnetic state. These findings are discussed with the scenario based on charge ordering at low temperature in the charge transfer insulator NiS2 pyrite, and also considering possible conducting surface states at low temperatures. At 300 K, the thermal conductivity decreases by 2.5 as x increases from 0.00 to 0.07, even though the latter is much more electrically conductive than the former. This considerably extends the range of values for the thermal conductivity of the MS2 pyrites, from the largest in FeS2 to the lowest in the present Ni1−xCuxS2 samples.