while the installation is in operation, measuring on a continuous basis over time electrical currents that flow through the installation and temperature values at predefined locations in the installation by means, respectively, of current sensors and temperature sensors disposed in the installation at the predefined locations, wherein the predefined locations are one or more upstream and/or downstream locations relative to one or more points of connection of conductors of the installation through which the electrical currents flow;

by an electronic data processing device and using a numerical model acquired beforehand, automatically computing, on a continuous basis, a numerical index representative of thermal properties of the installation, from differences between the measured temperature values and corresponding temperature values estimated by means of said model from the measured current values;

by the electronic processing device, detecting, on a continuous basis, a thermal anomaly when the computed numerical index differs from a reference value;

based on the detected thermal anomaly and using the predefined locations of the current sensors and temperature sensors, identifying an occurrence and a location of a defect or of a situation likely to lead to a defect at the identified location that can compromise safety of the installation; and

responding to the identification of the occurrence of the defect or situation by providing the identified location for correcting the defect or situation using the identified location, to mitigate a compromise of safety,

wherein the numerical model is representative of thermal properties of the electrical installation and is configured to associate current values measured by the current sensors with temperature values estimated for the locations at which the temperature sensors are positioned, the numerical model being previously parameterized by learning performed on the electrical installation; and

wherein the relationship between the temperature estimated for one of the locations and the current values measured in the installation is given by the following formula:

in which θ_tⁱ designates the temperature estimated for this location at a given instant, θ_t-1ⁱ designates the temperature estimated for this same location at a preceding instant, “n” is a statistical noise associated with the temperature sensor for this instant, “m” is the number of current sensors, “L” is the duration of the measurement window, “P” is the thermal power which depends on the measured currents and “α” and “β” are parameters of the numerical model.