There is much current debate about the way in which the earth's climate and temperature are responding to anthropogenic and natural forcing. In this paper we re-assess the current evidence at the globally averaged level by adopting a generic 'data-based mechanistic' modelling strategy that incorporates statistically efficient parameter estimation. This identifies a low order, differential equation model that explains how the global average surface temperature variation responds to the influences of total radiative forcing (TRF). The model response includes a novel, stochastic oscillatory component with a period of about 55 years (range 51.6-60 years) that appears to be associated with heat energy interchange between the atmosphere and the ocean. These 'quasi-cycle' oscillations, which account for the observed pauses in global temperature increase around 1880, 1940 and 2001, appear to be related to ocean dynamic responses, particularly the Atlantic multidecadal oscillation. The model explains 90% of the variance in the global average surface temperature anomaly and yields estimates of the equilibrium climate sensitivity (ECS) (2.29 °C with 5%-95% range 2.11 °C to 2.49 °C) and the transient climate response (TCR) (1.56 °C with 5%-95% range 1.43 °C to 1.68 °C), both of which are smaller than most previous estimates. When a high level of uncertainty in the TRF is taken into account, the ECS and TCR estimates are unchanged but the ranges are increased to 1.43 °C to 3.14 °C and 0.99 °C to 2.16 °C, respectively.