We study the alignment of grains subject to both radiative torques and pinwheel torques while accounting for thermal flipping of grains. By pinwheel torques we refer to all systematic torques that are fixed in grain body axes, including the radiative torques arising from scattering and absorption of isotropic radiation. We discuss new types of pinwheel torques, which are systematic torques arising from infrared emission and torques arising from the interaction of grains with ions and electrons in hot plasma. We show that both types of torques are long-lived, i.e. may exist longer than gaseous damping time. We compare these torques with the torques introduced by E. Purcell, namely, torques due to H$_2$ formation, the variation of accommodation coefficient for gaseous collisions and photoelectric emission. Furthermore, we revise the Lazarian & Draine model for grain thermal flipping. We calculate mean flipping timescale induced by Barnett and nuclear relaxation for both paramagnetic and superparamagnetic grains, in the presence of stochastic torques associated with pinwheel torques, e.g. the stochastic torques arising from H$_2$ formation, and gas bombardment. We show that the combined effect of internal relaxation and stochastic torques can result in fast flipping for sufficiently small grains and, because of this, they get thermally trapped, i.e. rotate thermally in spite of the presence of pinwheel torques. For sufficiently large grains, we show that the pinwheel torques can increase the degree of grain alignment achievable with the radiative torques by increasing the magnitude of the angular momentum of low attractor points and/or by driving grains to new high attractor points.

23 pages and 15 figures emulated ApJ style. Thermal flipping and trapping revised; paper accepted to ApJ