Context : Aims : We aim to study the physical conditions , particularly the excitation state , of the intermediate-temperature gas in protoplanetary nebulae and young planetary nebulae ( PPNe , PNe ) . The information that the observations of the different components deliver is of particular importance for understanding the evolution of these objects . Methods : We performed Herschel/HIFI observations of intermediate-excitation molecular lines in the far-infrared/submillimeter range in a sample of ten nebulae . The high spectral resolution provided by HIFI allows the accurate measurement of the line profiles . The dynamics and evolution of these nebulae are known to result from the presence of several gas components , notably fast bipolar outflows and slow shells ( that often are the fossil AGB shells ) , and the interaction between them . Because of the diverse kinematic properties of the different components , their emissions can be identified in the line profiles . The observation of these high-energy transitions allows an accurate study of the excitation conditions , particularly in the warm gas , which can not be properly studied from the low-energy lines . Results : We have detected FIR/sub-mm lines of several molecules , in particular of ^ { 12 } CO , ^ { 13 } CO , and H _ { 2 } O . Emission from other species , like NH _ { 3 } , OH , H _ { 2 } ^ { 18 } O , HCN , SiO , etc , has been also detected . Wide profiles showing sometimes spectacular line wings have been found . We have mainly studied the excitation properties of the high-velocity emission , which is known to come from fast bipolar outflows . From comparison with general theoretical predictions , we find that CRL 618 shows a particularly warm fast wind , with characteristic kinetic temperature T _ { k } \stackrel { > } { \scriptstyle \sim } 200 K. In contrast , the fast winds in OH 231.8+4.2 and NGC 6302 are cold , T _ { k } \sim 30 K. Other nebulae , like CRL 2688 , show intermediate temperatures , with characteristic values around 100 K. We also discuss how the complex structure of the nebulae can affect our estimates , considering two-component models . We argue that the differences in temperature in the different nebulae can be due to cooling after the gas acceleration ( that is probably due to shocks ) ; for instance , CRL 618 is a case of very recent acceleration , less than \sim 100 yr ago , while the fast gas in OH 231.8+4.2 was accelerated \sim 1000 yr ago . We also find indications that the densest gas tends to be cooler , which may be explained by the expected increase of the radiative cooling efficiency with the density . Conclusions :