We propose a new concept for insolation-driven temperature variability on orbital timescales. It relies on the modern relationship between insolation and temperature throughout the year. The method consists of (1) estimating empirical transfer functions between daily insolation and daily temperature and (2) applying these transfer functions on the long-term insolation to model the late Quaternary temperature evolution. On the basis of the observed insolation-temperature relationship, different temperature response regimes across the Earth are identified. Linear relationships dominate extratropical land areas whereas in midlatitude oceans, the seasonally varying mixed layer depth renders the temperature more sensitive to summer than to winter insolation. The temperature in monsoon regions and regions of seasonal sea ice cover also shows a seasonally varying response to insolation. These transfer functions characterize the shape of the seasonal cycle in temperature and influence the temperature evolution on orbital timescales by rectifying the insolation signal. On the basis of our seasonal template model, we estimate the temperature evolution of the last 750,000 years. The model largely reproduces the Holocene temperature trends as simulated by a coupled climate model. In the frequency domain, significant temperature variability in the eccentricity and semiprecession frequency band in the tropics is found. Midlatitudes are dominated by precession, and high latitudes are dominated by obliquity. Further, it is found that the expected frequency response highly depends on the location. Our local time-independent approach complements the global Milankovitch hypothesis (climate variations are driven by northern summer insolation) in explaining observed climate variability and potentially offers new insights in interpreting paleoclimate records. Copyright 2009 by the American Geophysical Union.