Lewis & Short

pillĕŏlus, i, m., and pillĕŏlum, i, n. dim. [pilleus], a small felt cap, a skull-cap: ut cum pilleolo (portes) soleas conviva tribulis, Hor. Ep. 1, 13, 15; Col. Arbor. 25; Hier. Ep. 85, n. 6; 64, n. 13.