Background
Over the past few decades, global warming at night has been about twice as great as warming during the day, which means, in the words of the authors, "that photosynthesis and respiration are necessarily responding to fundamentally different temperature signals."  In a prior study designed to explore the ramifications of this phenomenon Turnbull et al. (2002) determined "that elevated night temperatures at ambient CO2 partial pressures can increase leaf photosynthesis during the following day."  Hence, they decided to conduct another study to see if the same held true at elevated CO2 concentrations.

What was done
Four- to five-meter-tall cottonwood trees (Populus deltoides Bartr.) that had been grown for three years in air of different CO2 concentrations (420, 800 and 1200 ppm) in the three bays of the Biosphere 2 facility near Tucson, Arizona, USA, were maintained at three different nocturnal temperatures (15, 20 or 25°C) and a single constant daytime temperature (31 ± 1°C) in a short-term experiment in which maximum photosynthesis (Amax) rates at growth CO2 concentrations were measured.

What was learned
As nocturnal air temperature rose from 15 to 25°C, subsequent daytime Amax increased by 16% in air of 420 ppm CO2, 12% in air of 800 ppm CO2 and 4% in air of 1200 ppm CO2.

What it means
Turnbull et al. say these responses indicate that "at future elevated night temperatures suggested by global climate monitoring and modeling, net photosynthesis at elevated CO2 may be increased," and that "the response may saturate at CO2 partial pressures greater than double current ambient levels."  They further note that "the increase in A must result in an increase in net photosynthate potentially available for growth," and to emphasize this point, they state in their concluding paragraph that they thus "predict that plant growth responses to elevated CO2 may be enhanced at elevated night temperatures," which is more good news for the biosphere.

Reference
Turnbull, M.H., Murthy, R. and Griffin, K.L.  2002.  The relative impacts of daytime and night-time warming on photosynthetic capacity in Populus deltoides.  Plant, Cell and Environment 25: 1729-1737.