the usual suspects. It sounds as though you might have a preference file or other support file in Thunderbird that is corrupted.
The easiest solution is to remove the Thunderbird folder from the Libarary/Application Support location and the preference file from Preferences, and reinstall.
Note you don't have to delete these files, just move them out of the proper locations to either the Trash or to another location to test this out.
You might also try, as a first step, creating a new account, loading Thunderbird and seeing if that helped. If it did, then you know you should remove the old files and install a new instance of Thunderbird.
I am using Thunderbird 3.1.2 in a 2.66 GHz iMac with 4 GB of Ram on OSX 10.5.8. When Tbird is running, it maxes out the CPU usage. According to the iStat menus log, t averages around 70% of the CPU time. This has started recently and it drives the operating temperatures up substantially. If I quit T-bird, everything returns to normal.