## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Dwelling Number**} & **Set-Point Temperature,** \\  & **Average Seasonal Values [\({}^{\circ}\)C]** \\ \hline
1C & 18.6 \\
2A & 20.5 \\
3B & 21.4 \\
4C & 20.4 \\
5A & 19.3 \\
6B & 19.6 \\
7C & 19.6 \\
8A & 19.5 \\
9B & 22.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average seasonal values of set-point temperature used for the simulation of the base scenario. Figure 7: Simulated indoor temperature variation of apartments 2A, 5A and 8A in a representative week of the heating season, base scenario. is very effective and set-point temperatures are reached in less than about 15 min. Generally speaking, this limited warm-up time mainly depends on the time constant of the heating system and, to a lesser extent, on that of the building. Obviously, this heating transient is not representative of the indoor comfort conditions of the room, that are determined by both the indoor air temperature and the mean radiant temperature, which depends on the thermal mass of the building. On the other hand, the low thermal mass of the building is the cause of high temperature drops when the generator is turned off, especially in apartments in disadvantaged positions, despite their heat thefts from adjacent dwellings. Finally, it is worth to observe the behavior of the building during non-heating hours with the related heat exchanges among apartments. For the purpose of evaluating the heat gains and losses due to a change of operation, the authors simulated two different scenarios in addition to the base one: (i) scenario a, in which only apartment 5A was assumed to be unheated; (ii) scenario b, in which only apartment 2A was assumed to be unheated. In both cases, the set-point temperatures of all other apartments remained unchanged with respect to the base scenario. These were chosen as representative of the most and the least favored positions of block A (but similar considerations can be made for block B except for minor changes due to the different orientation): in fact, apartment 5A is located in the second floor and surrounded by heated spaces (apartments 2A, 6B, 4C and 8A) while apartment 2A is located at the first floor and its uninsulated floor is completely exposed to outdoor temperature. Table 6 shows the results obtained from switching off the heating system of the dwelling 5A (scenario a). Obviously, in this case all the thermal zones adjacent to apartment 5A give energy to it, with apartment 2A and 8A giving, respectively, 8.5% and 5.2% of their total energy need for space heating (in fact these apartments have the largest heat exchange surfaces). Overall, apartment 5A is able to steal 1249 kWh from its neighbors, which would have accounted for 25% of its energy consumption in the base scenario. Referring to Figure 9, it is important to highlight that when the heating system is not working, in some hours of the week, apartment 5A still has its indoor air temperature higher than the one of both adjacent dwellings, confirming again the existence of an inversion in the direction of the heat flows already highlighted in the base scenario. In this scenario, the average seasonal difference of indoor temperature between apartment 5A and the other heated apartment is about 2.6 \({}^{\circ}\)C. Table 7 shows the results obtained from switching off the heating system of the dwelling 2A (scenario b) while Figure 10 shows the trend of the indoor temperature of the investigated apartments in a representative week of the heating season. Figure 8: Simulated indoor temperature trends of apartments 2A, 5A and 8A during the warm-up time of a representative day: (**a**) from 5.00 a.m. to 7:00 a.m.; (**b**) from 14:00 p.m.to 16:00 p.m. The results show that apartment 2A is always able to gain heat from its neighbors (apartments 5A, 1C, 3B,) since its indoor temperature is always lower than that of the other ones, stealing up to 13.6% of the total energy need for space heating of apartment 5A.