McGhee, Masket, Shor, Rogers and McCarty have written this article for AJPS.  Here is the abstract:

Many theoretical and empirical accounts of representation argue that primary elections are a polarizing influence. Likewise, many reformers advocate opening party nominations to nonmembers as a way of increasing the number of moderate elected officials. Data and measurement constraints, however, have limited the range of empirical tests of this argument. We marry a unique new data set of state legislator ideal points to a detailed accounting of primary systems in the United States to gauge the effect of primary systems on polarization. We find that the openness of a primary election has little, if any, effect on the extremism of the politicians it produces.