OP stated "The problem is, half the time when I record video the camera stops about a minute in and says "recording stopped automatically"." This should not be an overheating issue.
As others have pointed out, it is likely the card. Also, be aware there are some limitations on how much you can record, even with the best of memory cards. More than 12 minutes can be recorded but there are some limitations. When the file size reaches 4 GB, recording will automatically stop. That means that at 1920x1080 dpi and 1280x720 dpi the maximum recording time of a single movie clip is about 12 minutes. At 640x480 dpi it is about 24 minutes. I think there is also an auto-restart function in the 60D so it will start again and you loose only a few seconds of video.
The capacity of the card differs in recorded time; at 1920x1080 dpi or 1280x720 dpi you can stuff 44 minutes total of video onto a 16 gig card. At 640x480 dpi or crop 640x480 dpi this goes up to 1 hour 32 minutes. However, the 60D English manual movie section states "The maximum recording time of one movie clip is 29 min. 59 sec. Depending on the subject and the increase in the camera's internal temperature, the movie shooting might stop sooner than 29 min. 59 sec.' [60D manual, page 181]
This is not just the Canon line, Pentax for instance states "Like competing DSLRs, the Pentax K-5 also monitors sensor temperature during recording, and will halt capture if the temperature rises beyond a certain threshold." A reputable source also states "This limitation is due to the different (European) import duty rates for still and video cameras." There is no reference made to differing duty rates of product entering the United States however. So there may really be two limitations, one the 29 min 59 seconds limitation imposed legally, and a sensor temperature issue that might also be reached in some rare circumstance.