What was done
Rice (Oryza sativa) was grown in SPAR units in Florida, USA, with daytime atmospheric CO2 concentrations of 350 and 700 ppm, as part of a long-term experiment studying the effects of elevated CO2 and water stress on rice.  In this paper, the authors studied the effects of daytime CO2 enrichment on nighttime dark respiration as a function of nighttime CO2 concentration and temperature.

What was learned
Rates of dark respiration decreased significantly with increasing nighttime CO2 concentration, regardless of daytime CO2 growth conditions, at nighttime temperatures above 21°C.  However, dark respiration rates were consistently higher for plants grown at 700, rather than 350, ppm CO2, most likely due to their greater biomass and leaf carbohydrate contents; for when dark respiration rates were measured at the growth concentrations of plants grown at 350 and 700 ppm CO2, their average rates were not significantly different, regardless of nighttime temperature.

What it means
As the atmospheric CO2 concentration rises, it is likely that nighttime respiratory carbon losses from rice plants will be reduced, with greater reductions occurring at higher, rather than lower, air temperatures.  Thus, rice should increase its diurnal net uptake of carbon, which should lead to greater biomass production and, possibly, increases in yield, as has been commonly reported in the literature.