I like the Ol' run your water, add a few pounds of grain, stir, add a few pounds of grain, stir, until the process is complete method. I don't worry about preheating the tun either, but I will leave the grain and tun in the house at room temp untul I'm ready to mash in. This keeps the strike temp more consistant.
More geared to the OPs question. I often crush my grains as part as my brew day set up, which is done the evening before brewing. Why not just crush the grains and leave them in a bucket with a lid?