There seems to be some less than clear information in this thread. Not sure I can help to clarify things or not, but here goes.
Supply cable resistance is extremely unlikely to be of any concern for a UK installation. The regs here specify that the installer has to ensure that the voltage drop at the charge point end of the cable must not exceed 5% of the nominal supply voltage when under maximum load (for completeness, the voltage drop allowable on a lighting circuit is 3%, mainly to avoid visible fluctuations in light level when additional lights are switched on or off).
In practice, the voltage drop is very unlikely to be anywhere near 5% for a charge point installation, as the cable is normally over-sized. The manufacturers instructions (MIs) take precedence over the wiring regulations for some things, and many specify that the minimum supply cable for a 32 A charge point shall be 6mm², which is normally a heavier gauge cable than is strictly necessary for most domestic charge point installations. As an example, a 20m run of 6mm² cable will give a voltage drop of about 1.2% well under the requirement in the regs. There's a handy voltage drop calculator on the TCL website:
Voltage Drop Calculator | TLC Electrical (I've no connection to them, other than as a customer).
Whilst it's true that cable (and whole circuit) resistance will increase as the temperature increases, this will have no effect at all on the current drawn in the case of a charge point, as the charger (in the car) will try to draw the current set by the Control Pilot duty cycle, irrespective of small changes in the apparent supply voltage. Anyway the temperature increase in the cable from the load current is likely to be pretty small, because most UK installations will most probably have oversize cabling (largely to reduce the temperature rise from what may be a sustained high current load) in accordance with the charge point MIs.
The factors that cause over-current devices to trip at elevated temperatures are primarily self-heating within the over-current device itself in combination with the local ambient temperature inside the device enclosure. Over-current devices have two internal overload protection mechanisms. One is a fast-acting magnetic trip, that responds to rapid and severe over-current events, the second is a thermal over-current trip, that responds more slowly to a sustained overload condition. As it's name implies, a thermal overload trip works by an internal element heating up, as a result of the current passing through it, causing a bimetallic strip to deform and initiate the rapid trip mechanism, that breaks the circuit.
One side effect of this long duration overload sensing method, is that it is temperature sensitive. The warmer the area around the device, the faster it will tend to trip under a modest overload. One significant issue, and a very good reason for installing a charge point over-current protection device in it's own enclosure, is that all devices like this get warm under load, so if you have several, in close proximity to each other, within the same enclosure, then at times when several circuits are fairly heavily loaded the devices will get a bit warm, making them a bit more sensitive (as shown in those curves posted above).
When it comes to the cause of a trip in a charge point circuit, if the protection device is an RCBO, a combined over-current and residual current protection device (which it may well be) then it can be difficult to quickly determine whether it has tripped because of an over-current event, or because of a residual current event.
In this case diagnosis is made easier because the residual current device is separate from the over-current device, and it is the over current device that has tripped. The explanation given that the trip might have been caused by a surge is certainly plausible. Although supply lines are protected to some extent from lightning strikes, there can be very short duration voltage surges, either induced by nearby lightning strikes, or from unusual local network events, such as a heavy load being suddenly disconnected. If the voltage surges, the the instantaneous current through the over-current device might exceed the fast-acting magnetic trip device limit.
Although it seems that this installation is sensibly fitted in its own dedicated enclosure, so isn't going to get warmed up by adjacent over-current devices, it is possible that it may have been getting warm for other reasons. Apart from external heating from hot weather, other heat sources etc, the most common reason for heat build up in enclosures like this is if the connections aren't tight. Despite warning labels and a lot of emphasis during training about the critical importance of ensuring terminations are correctly torqued up, finding loose connections that have clearly been running hot is all too common. It's so common that the regulations were amended a few years ago to ban the use of plastic enclosures in dwellings, so now they all have to be fireproof (usually metal). This hasn't stopped the problem of loose terminations, but does reduce the risk that loose termination might start a fire.
It's just a few minutes work for a competent person to isolate the power and check the torque on the terminations, but in the meantime, it wouldn't hurt to point an infrared thermometer directly at the MCB (miniature circuit breaker) that has tripped in the past, after the car has been charging at maximum current for an hour or two. If its temperature is more than about 30 degrees above ambient, I'd be inclined to suspect that something is awry, and report this to the installer. Warming up by a few degrees above ambient is normal, though, and nothing to worry about, it's when the case of the MCB itself gets hot that I'd be concerned.
