I have a 2 year old Toshiba and had the same problem. I'm not a real techy guy but this is what I've figured out from reading countless threads and putting all the suggestions I've read into practice. This ate least let's me play games now and not have awful wait time for turns to complete or graphics to load. I also bought a laptop cooler.
Update your video drivers, that's a given. I had to uninstall my Toshiba drivers and use the generic ones from the Intel website. I have the graphics settings in Civ set to the lowest res (not sure what it is) I turn off battle animations, etc... I zoom all the way in during gameplay and city views. At the beginning of every other turn I switch to strategic view, zoom out, and survey everything (resources, units, etc....) to get a lay of the land, then I zoom back in, get back to standard view, and complete my turn. Just to keep turns shorter and to further ease the strain on my laptops resources I play small maps.
None of this is ideal but at least I can play now. Hope some of that is helpful.