Ink jet apparatus for use with hot melt ink has an integrally connected ink jet head and reservoir system, the reservoir system having a sloping flow path (58) between an inlet position and a sump (60) from which ink is drawn to the head, the reservoir being housed in a housing (40) of good heat conductivity material with a heater (51) connected thereto, and further having one or more heat conducting elements (55, 57) positioned between the inlet position and the sump, which elements are constructed to act both as baffles and as heat conducting fins.