A heat press includes a screen printing head and a stamp unit. The stamp unit includes a frame, carriages, a support, and a platen or ironer. A horizontal position of the platen relative to the screen printing head can be adjusted by unlocking carriages from guide rails and sliding the carriages while the frame remains attached to the screen printing head. Also, the platen is coupled to the support so that a horizontal position of the platen relative to the support is fixed, and a vertical position of the platen relative to the support is floating. The heat press is suitable for applying a print on a substrate, such as a stack of fabric layers of different sizes.