A warmer climate will likely leads to warmer soils, which, in turn accelerate biological and chemical processes contained therein. Break-down of carbon-containing material in the soil to produce carbon dioxide is one such process that is temperature dependent. One view is that warmer soils lead to faster decomposition of organic matter and hence more CO2 emitted from the soil as a result of global warming. This increase in CO2 efflux from the soil (called soil respiration) further enhances the greenhouse effect and leads to additional warming and even more loss of soil CO2 , a so-called positive feedback effect.
Melillo et al (2002) tested this idea by conducting a 10-year experiment at Harvard Forest where they buried heating cables in the ground and kept it 5oC warmer than it otherwise would have been. They compared heated plots with plots having no additional heating (called the "control" plots). They measured CO2 coming out of the soil (soil CO2 efflux) from April through November each year. They found a 28% increase in CO2 efflux for the first 6 years and then the effect of heating was diminished to only about 5%.
The authors also measured nitrogen changes in the ecosystem during the experiment. They found that, like many terrestrial ecosystems, the Harvard Forest soils had less nitrogen than could be used by the vegetation. But the warming accelerated the availability of soil nitrogen for the trees, which led to increased tree growth (e.g., more carbon stored in trees).
Melillo et al (2002) concluded that warming temporarily increases carbon loss from soils but that the warming also increases carbon storage as wood in trees, in an amount that compensates for the soil loss. They did not consider other effects that might accompany warming such as drier conditions.
Reference
Melillo, J. M., P. A. Steudler, J. D. Aber, K. Newkirk, H. Lux, F. P. Bowles, C. Catricala, A. Magill, T. Ahrens, and S. Morrisseau, 2002: Soil warming and carbon-cycle feedbacks to the climate system. Science 298, 2173-2176.