Global mean surface temperature (GMST) is the most widely cited climate change indicator, with trends at multiple time scales figuring prominently in IPCC reports. Here we present an alternative non-linear continuous local regression (LOESS) method using multidecadal windows and evaluate GMST changes (DGMST) for five operational blended land-ocean surface temperature datasets. The best estimate of DGMST from pre-industrial (1850—1900) to 2018 is 1.12°C [0.93 – 1.27], based on three spatially complete global series. The IPCC’s linear trend methodology applied to the three series assessed in IPCC AR5 yields 0.99°C [0.80 – 1.18], with much of the difference attributable to the trend methodology. LOESS yields lower estimates than linear over 1951-2018, and virtually identical results over 1979-2018. LOESS outperforms linear fits when validated against a 20- or 30-year averages relative to pre-industrial. We show that it reliably reproduces the known forced changes in DGMST when applied to output of a large model ensemble, except for years affected by large volcanic eruptions. Furthermore, our estimate of statistical uncertainties from a fit are reliable, by comparing against the ensemble spread. We also present a simple and easily updated remaining carbon budget to stay below 1.5 or 2°C, based on a global surface air temperature (SAT) estimate derived from model-based adjustment of blended full global GMST. Finally we perform a preliminary evaluation of recent short-term fluctuation. Continuous non-linear trend estimation offers a compelling alternative to linear trends for the assessment of long-term observational GMST series at multiple time scales.