Estimates for the total solar irradiance (TSI) during the 17th-century Maunder Minimum published in the last few years have pointed towards a TSI difference of 0.2–0.7 W m−2 as compared to the 2008/2009 solar minimum. Two recent studies, however, give anomalies which differ from this emerging consensus. The first study indicates an even smaller TSI difference, placing the Maunder Minimum TSI on the same level as the 2008/2009 minimum. The second study on the other hand suggests a very large TSI difference of 5.8 W m−2. Here I use coupled climate simulations to assess the implications of these two estimates on Northern-hemisphere surface air temperatures over the past millennium. Using a solar forcing corresponding to the estimate of the first study, simulated Northern-hemisphere temperatures over the past millennium are consistent with reconstructed surface air temperatures. The large TSI differences between times of high and low solar activity as suggested by the second study, however, yield temperatures during all past grand solar minima that are too low, an excessive variance in Northern-hemisphere temperature on timescales of 50–100 years as compared to reconstructions, and temperatures during the first half of the 20th century which are too low and inconsistent with the instrumental temperature record. In summary this suggests a more moderate TSI difference of less than 1 W m−2 and possibly as low as 0–0.3 W m−2.