In an automatic recording instrument having a thermal recording-pen to record on a heat sensitive recording-paper, an operational amplifier output supplies the heating current to the thermal pen through a resistor. A non-linear transfer element receives the output voltage of the amplifier and delivers a voltage having a predetermined non-linear relation to its input. The voltage difference between the output of the non-linear transfer element and the junction point of the thermal pen to the resistor is feedback connected to the input of the amplifier. When the relative velocity between the pen and the paper is increased, the input voltage of the amplifier is increased to increase the output voltage, and when the output voltage is increased, the resistance of the thermal pen is increased to balance to the output of the non-linear transfer element for reducing the input to the amplifier. This means that the heated temperature of the thermal pen is raised when the pen moves faster on the paper and a constant thickness of the recording is maintained in a wide range of the relative velocity between the pen and the paper.