## 4 Results
### Overtemperature Analysis  
An analysis was carried out on the operative temperature in the point P (Figure 2) in the period from December to February, considering the degree hours criteria described in Anne F of EN 15251 (2007) [39]. A temperature range was defined and the degree hours outside the upper boundary of the range (\(T_{ul}\)) was used as a performance indicator of the building for the heating season in relation to the overtemperature. The weighting time for overtemperature WF\({}^{+}\) can be calculated as:  
\[\text{WF}^{+}=\sum(T_{o}-T_{o,ul})\text{ for }T_{o}>T_{o,ul} \tag{12}\]  
Since the simulations have been performed maintaining in the convective ideal case the air temperature constant at 20 \({}^{\circ}\)C, the operative temperature differs in all cases. Hence, a specific range was defined for each radiant case, centred on the mean value of the operative temperature, which is the same of the ideal convective cases, and with an amplitude of 1.0 \({}^{\circ}\)C (i.e. \(\pm 0.5\)\({}^{\circ}\)C). A small band was chosen, with the same amplitude of the on-off thermostat, since the purpose was not the evaluation of comfort conditions, but simply the evaluation of the periods with the operative temperature rising outside the control band of the air temperature and the comparison of these periods with different envelopes and type of radiant systems, as well as the comparison between the building with the radiant systems and the same building with an ideal convective heating system. A larger band was not suitable for a fully exhaustive evaluation for this purpose, since it was found that, in the worst cases (well-insulated timber envelope and light envelope with dry floor system), the operative temperature exceeded more than 1.5 \({}^{\circ}\)C its mean value for only about 3% of the time, i.e. no discomfort has been found for overheating in all the cases.  
In Figure 11 the WF\({}^{+}\) calculated from the results of the radiant simulations are represented. As can be noticed, the constant supply water temperature control modality always gives a higher WF\({}^{+}\) than the climatic control modality, except for the well-insulated buildings, where the WF\({}^{+}\) are similar. The ceiling systems present a WF\({}^{+}\) which is, on average, more than five times the WF\({}^{+}\) of the floor systems in the non-insulated building and 2.5 times in the insulated and well-insulated masonry buildings. In the well-insulated lighter buildings the dry-floor system presents the highest WF\({}^{+}\), almost 1.5 times the WF\({}^{+}\) of the wet-floor and ceiling systems.  
It is interesting to notice that the 50% of the WF\({}^{+}\) of the well-insulated light buildings can be already found in the ideal convective simulations. This percentage decreases to 27% for the well-insulated masonry buildings, 12% percent for the insulated buildings and only 2% for the non-insulated buildings. In a convective system controlled with an on-off band like the simulated radiant systems, these percentages would certainly be higher, showing that the problem of overtemperature in well-insulated buildings is not strictly related to the radiant system itself, but it is inevitable especially in the case of light structures (even in ideal conditions); secondly, the control modality may affect the overtemperature.  
In Figure 12 the value WF\({}^{+}\)/h\({}^{+}\) of the overtemperature is represented; h\({}^{+}\) is the number of hours which contribute to the overall value of WF\({}^{+}\), i.e., the number of hours in which the operative temperature exceeds the threshold value defined; this parameter can be named overtemperature intensity. In the insulated buildings the overtemperature intensity is the same of the ideal convective cases, except for the constant supply water temperature ceiling systems which show much higher