This paper discusses the advantages and disadvantages of the different methods that separate net ecosystem exchange (NEE) into its major components, gross ecosystem carbon uptake (GEP) and ecosystem respiration (R_eco). In particular, we analyse the effect of the extrapolation of night-time values of ecosystem respiration into the daytime; this is usually done with a temperature response function that is derived from long-term data sets. For this analysis, we used 16 one-year-long data sets of carbon dioxide exchange measurements from European and US-American eddy covariance networks. These sites span from the boreal to Mediterranean climates, and include deciduous and evergreen forest, scrubland and crop ecosystems. We show that the temperature sensitivity of R_eco, derived from long-term (annual) data sets, does not reflect the short-term temperature sensitivity that is effective when extrapolating from night- to daytime. Specifically, in summer active ecosystems the long-term temperature sensitivity exceeds the short-term sensitivity. Thus, in those ecosystems, the application of a long-term temperature sensitivity to the extrapolation of respiration from night to day leads to a systematic overestimation of ecosystem respiration from half-hourly to annual time-scales, which can reach >25% for an annual budget and which consequently affects estimates of GEP. Conversely, in summer passive (Mediterranean) ecosystems, the long-term temperature sensitivity is lower than the short-term temperature sensitivity resulting in underestimation of annual sums of respiration. We introduce a new generic algorithm that derives a short-term temperature sensitivity of R_eco from eddy covariance data that applies this to the extrapolation from night- to daytime, and that further performs a filling of data gaps that exploits both, the covariance between fluxes and meteorological drivers and the temporal structure of the fluxes. While this algorithm should give less biased estimates of GEP and R_eco, we discuss the remaining biases and recommend that eddy covariance measurements are still backed by ancillary flux measurements that can reduce the uncertainties inherent in the eddy covariance data.