Most modern coolant temperature gauges are actually multi-function warning lights masquerading as gauges. They will read in a linear fashion until the minimum acceptable "warm" temperature has been reached - then the gauge will be fed the right voltage to sit it on the centre of the gauge - no matter how much the temperature fluctuates - as long as it sits within the normal range the gauge will not move - so you won't get a feel for how efficiently your cooling system is functioning as you did in the "old days". Plug in a OBDII reader and watch the temp fluctuate quite markedly as proof - the coolant temp gauge will not budge.
Most temp gauges now have four modes above the warm up phase: 1) "normal" (needle pinned in the middle of the gauge) once the temperature is into the normal range. 2) "hot" Once you are over the normal range, depending on the car manufacturer, most gauges will either read an analogue approximation of the temp as to when it is in the normal to over heated range - or will just sit at 3/4 - perhaps with an amber light. 3) "overheating" above "hot" will put the gauge in the red which is the "stop as soon as possible" warning - often with solid red light. 4) "Critical" temp, where a red warning light with flash and/or system message appears- this is the temperature at which the manufacture would expect engine damage to occur. Not sure if the P38s has a separate 3&4 like most modern cars, or just a single overheating "in the red" mode.
What always ****ed me off with P38s is they beep at you for everything, door not shut? Beep, bonnet not closed? Beep, key in ignition? Beep. Lights left on? Beep, sunroof not shut? Beep. Transmission left in gear? Beep. But engine temp gauge pinned in the red, potentially leaving you with a £5K repair bill? Nothing nada - not a squeak! Aghhhhh!!