Dust particulates immersed in a quasineutral plasma can emit electrons in several important applications. Once electron emission becomes strong enough, the dust enters the positively charged regime where the conventional orbital-motion-limited (OML) theory can break down due to potential-well effects on trapped electrons. A minimal modification of the trapped-passing boundary approximation in the so-called OML(+) approach is shown to accurately predict the dust charge and heat collection flux for a wide range of dust size and temperature.