Dallas Burtraw, Richard Sweeney & Margaret Walls (all of Resources for the Future, Washington, D.C.) have published The Incidence of U.S. Climate Policy: Alternative Uses of Revenues from a Cap-and-Trade Auction, 62 Nat'l TaxJ. 497 (2009).  Here is the abstract:

This paper evaluates the costs to households of a carbon dioxide (CO2) cap-and-trade program. We find important variation in the distribution of costs of the policy across 11 regions of the country and across income deciles. The introduction of a price on CO2 emissions is regressive, but this may be outweighed by the distributional effects of CO2 emissions allowances. We evaluate five alternatives for returning any revenues from auctioning emissions allowances—three are progressive (expansion of the Earned Income Tax Credit and two cap-and-dividend approaches), while the others are either neutral (a reduction in payroll taxes) or amplify regressivity (a reduction in the income tax). Regional differences are most substantial for low-income households.