A recent paper by Austrian scientists seeks to answer this question:
Weihs P, Rennhofer M, Baumgartner DJ, Gadermaier J, Wagner JE, Gehring JE, Laube W.
Potential impact of contrails on solar energy gain.
Atmospheric Measurement Techniques. 2015 Mar 5;8(3):1089-96.
It contains very interesting...