When a thought 'crosses your mind', does it literally cross between left and right cerebral hemispheres?
Neuroscience doesn't really have a clear model for what a "thought" consists of exactly. Certain processes that are involved in thought have begun to be mapped--for example, this recent paper talks about a model for how the brain associates location in space with it's own mental map (http://www.ncbi.nlm.nih.gov/pubmed/24462102, I'll try to find something related that's not behind a paywall...). This one doesn't address your particular problem though, they only measured activity on one side of the brain. So basically, it might be possible to partially answer your question for more specific brain processes, but different kinds of "thoughts" are processed in different ways.

And of course I am also conflating impulses crossing the corpus callosum with the thoughts themselves, but I don't think this is really accurate. The most popular models in the labs I'm familiar with suggest that a "thought" is composed of a bunch of neural activity taken together rather than the activities of a few neurons on their own. But that might ultimately just be arguing semantics.