The invention relates to a fluid-heating device (1) comprising: a fluid circulation conduit (5), electric heating means (4), and a switch (6) which can be moved selectively between a configuration in which the electric heating means are powered and a configuration in which the electric power being supplied to the electric heating means is cut off. The invention also comprises a thermally-fusible part (7) which is intended to be heated by the electric heating means when in operation and which is designed (i) to fuse at least partially when at least one area (8) of the electric heating means exceeds a critical temperature threshold and (ii) to move the switch (6) from the power supply configuration to the power cut-off configuration.