It's a problem on that model with the DC/DC convertor. You need to replace the left side IO board entirely and I also recommend you replace the AC/DC power pack as well.
If you measure the current coming out of the charging circuit it will be over by about 10 amps. We have a pile of these with the same problem but most aren't worth the repair cost in 2013 dollars.
You really need to fix this before you get a fire. At the very least leave the battery out for now when it's unattended.
Installing MacBook Pro 15" Core Duo Model A1150 Left I/O Board - iFixit