This entry – about thermal management nuances for the N series. This also applies to, for example, N52 and other engines.  On the internet, there are numerous posts in which the users are complaining regarding:

a. slow warming up of the engine;

b. the working temperature of the engine for all or almost all time is lowered (very often, Mapped mode is mentioned).
Unfortunately, there is almost no valuable advice or solutions. So, I believe the information below will be useful for many BMW users. 

First (especially – if the engine warms up slowly): make sure that the thermostat is closed when it needs to be closed. For this test:
a. disconnect the heating plug of the thermostat;
b. warm up the engine. By using a digital thermometer or thermal camera, measure the temperature (before) of the thermostat and after it (a pipe to the cooling radiator, inlet region of the radiator).
Till the moment when the thermostat opens (around 90 oC), the pipe to the radiator and the radiator itself should be cold! If the radiator is even slightly warm, replace the thermostat. Install only OEM thermostat, it is not expensive. 


The reasons for the Mapped mode (summarized by my experience, the information from the manufacturer is close to 0):
a. a clogged cooling radiator; problems with the thermostat (it is stuck, tends to get stuck, is not closing, is not opening completely). Clean the cooling radiator with the high-pressure water jet (Karcher). Replace the thermostat. Check the heating element of the thermostat (its resistance, by measuring with the Ommeter: very approximately – several Ohm to 10+ Ohm). If the resistance of the element is higher than the several tens of Ohm or it can not be measured – replace the heating element. The same – replace the element if DME has recorded the error message regarding it (even if the error message is passive, it means – problem is sporadic);
b. reduced oil temperature, poor oil quality, problems with the oil level/quality sensor, and/or communication with it. If there are error messages regarding the BSD connection (water pump, IBS sensor, or other BSD “customer”), they should be solved first! BSD problems can create problems with the oil parameter reading. Check the oil temperature reading in INPA. If the engine is properly warmed up (and during the warm-up), the oil temperature is at least 10 oC higher than the temperature of the cooling liquid. If the oil temperature is lowered – replace the oil parameter sensor.  Change the oil not less than after each 10’000 km and use only OEM oil filters! Evaluate the oil quality parameter (if available – also in ISTA). If the oil quality is low, change the oil and filter immediately!
c. any problems with the water pump should be solved immediately. Even the error message regarding “only” communication means that the water pump works in emergency mode, and its flowrate is not managed. A damaged water pump can stop at any moment, and then the engine will overheat for several minutes. 
d. any problems with the cooling blinds too can cause the activation of the Mapped mode. Solve the problems with these flaps or dismantle them – then it is mandatory to delete them from FA.
e. lowered oil pressure at the start moment or in any driving conditions. If DME notices low oil pressure for a too long time when starting the engine or lowered oil pressure (by high oil temperatures), DME will switch the Mapped mode on. Unfortunately (if the lowered oil pressure is not for a longer time and at least 2 times below the threshold), in these cases, no error messages will be recorded. For N43/N53 series engines, the oil pressure (required/actual) during start can be observed; by specific nuances, it is possible to identify what DME “does not like” during the moment of the engine start. For simpler engines, unfortunately, such diagnostics are burdened. What to do? Change the oil regularly, use OEM oil filters, and use the appropriate oil of high quality (don’t use “more liquid” or some “racing” oils). Make sure that the valve below the oil filter is closing, and also, after a longer stand-still, the filter is full of oil (the oil has not congealed in the crankcase). 
f. reduced efficiency of the CO catalytic converters. If DME identifies reduced efficiency of the CO catalytic converters, it switches to Mapped mode and heats the catalytic converters in a forced mode. Yes, pass/fail data for this procedure can be observed via OBD Mode 9 (usually available in INPA), but the diagnostics are not so simple here. The discontinued tests are counted as failed ones, no freeze-frame data, etc. Read more here and here.
g. problems with the Rail pressure. This applies to DI engines – if DME notices problems in maintaining the Rail pressure in the increased temperature mode, it switches on the Mapped mode, to “solve” this problem. 
h. misfires, problems with the fuel mixture (if they are identified by high oil temperature). Also, in these cases, DME switches to Mapped mode to reduce the amount of emissions (heats the CO catalytic converters in an increased amount). Unfortunately, for N52 and older engines, no misfire counters are available. 
i. In idle, if the car is standing still longer than several minutes, DME switches on the Mappe mode. It is done to reduce the emissions. In this mode, DME increasingly heats up the CO catalytic converters. 
Remember: Mapped mode is 80 oC. If everything is okay with the cooling system, DME will maintain this temperature very precisely. If the temperature differs from 79 .. 81 oC (and during several tens of seconds does not stabilise to 80 oC) – it is not Mapped mode (or the engine has problems maintaining this temperature, or – DME has switched from Mapped mode to some other mode, ir its “underway” to it).
Another nuance: use INPA or ISTA to read the temperature. No one (I assume, even the developers of these tools) knows what kind of temperature the menu is indicated by some tool developed by a 3rd party. Yes, many of them are developed on the base of INPA scripts, but there are many mistakes in them.
And finally – after each repair (including problems with the thermostat, radiator cleaning, repair of the cooling blinds, etc.) perform the re-adaptation of the engine! How to do it – read here. Remember – re-adaptation of the engine is NOT only deleting the old adaptations!
After re-adaptation (especially, if DME previously has noticed problems with the thermal management), during the first driving sessions, DME will perform test procedures of the thermal management. During these procedures, DME switches on the Mapped mode – it is normal. Also the DME of a completely correctly working engine time after time, as a routine check, checks the thermal management by switching on and off the Mapped mode. Unfortunately, there have been no notices regarding the activation of such tests. 
Some useful information you will find here, here, and here and here.