Hi Christian!
Your perspective is a bit too "girly" or "girlish." Sorry!
I will try to provide a more in-depth analysis here to estimate the heat balance of the TDIs.
Assuming an idle fuel consumption of 0.5 liters per hour, the following energy balance results:
Heating value of diesel: approximately 44,400,000 J/kg.
Density of diesel fuel: approximately 0.85 kg/l.
Energy input per hour: 44,400,000 J/kg * 0.85 kg/l * 0.5 l/h = 18,870,000 J/h
corresponds to an input power (chemical/thermal): P_input = 18,870,000 / 3,600 s = 5.24 kW.
If this power output were available solely (e.g., via STH) for heating the cabin, then no TDI drivers or passengers should experience coldness during the winter.
However, a certain portion of this power is converted into mechanical power to overcome the frictional losses of the engine and to drive the auxiliary components. However, it should be possible to recover these frictional losses and convert them back into "useful heat."
Now, 4 effects are responsible for the fact that this immense heating power is not available for heating the cabin.
1. Heat radiation of the unit.
2. Heat dissipation from the unit through heat conduction and transfer to the environment.
3. Heat loss through exhaust gases.
4. Heat capacity of the engine.
Performing a reasonable estimate for points 1 and 2 is not trivial, as it requires knowledge of a large number of parameters.
An estimate for the heat losses through the exhaust gases could be calculated as follows:
Idle speed: n = 900 RPM.
special Density of air: ρ = 1.25 kg/m³
special Specific heat capacity of air: 1.005 kJ/(kg*K)
Estimated exhaust gas temperature at idle: T = 150°C.
Intake air temperature: 0°C.
Air mass flow rate: m' = 900/60 * 0.5 * 1.9 / 1000 * 1.25 = 0.0178 kg/s
Required heat power for heating the intake air: Pheiz = 0.0178 * 1.005 * 150 = 2.68 kW
This indicates that approximately 50% of the heat supplied during idle operation is lost through the exhaust

.
Assuming that, during a cold start, the engine block has the same temperature as the surrounding environment (in the example provided, 0°C), approximately 2.5 kW of heating power would initially be available to heat up the block.
As soon as the engine's temperature rises slightly above the ambient temperature, heat is dissipated through thermal radiation and conduction, and the amount of heat dissipated increases as the engine block's temperature rises.
Assuming a mass of approximately 100 kg for the engine, including coolant, oil, and attachments, a simple estimate of the warm-up time can be made based on the thermal capacity of the engine.
It is relatively difficult to determine a specific heat capacity for an engine because the mass is distributed across various materials such as steel, cast iron, aluminum, water, and oil. In the following, I will assume an average heat capacity of approximately 0.6 kJ/kg.
This results in a heat capacity of C = 100 kg * 0.6 kJ/(kg*K) = 60 kJ/K for the engine.
With ideal thermal insulation of the unit against heat conduction and heat radiation, and without heat removal via the heating heat exchanger, the ideal warm-up time in idle mode would be:
t heating = (60 kJ/K * 80 K) / 2.5 kW = 1920 s = 32 min
Now, however, the real-world conditions come into play. As soon as a noticeable temperature difference exists between the object and the surrounding air, a significant amount of heat is released to the environment.
So, letting the cold engine run for an hour in idle might not bring it up to operating temperature.
During the warm-up phase of a moving vehicle, the engine block is additionally cooled by the cold ambient air flowing over it due to the vehicle's speed. This significantly improves heat transfer, which helps to "cool down" the engine.
Regards,
Alex.
AUDI A3 1.9 TDI, EZ 12/96, ursprüglich MKB AGR, umgebaut zum AHF mit GT1749V-Lader, verkauft mit 250tkm
Golf 4 1.9 TDI, EZ 1/98, MKB ALH, jetzt auch mit GT1749V-Lader, verkauft mit 300tkm
Touran 1.9 TDI, EZ 09/2004
Audi A4 Avant 2.0 TDI, EZ 03/2010