macbook very hot- fan going on early

I have fairly early macbook-but second generation:

Model Identifier: MacBook2,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 4 MB
Memory: 2 GB
Bus Speed: 667 MHz
Boot ROM Version: MB21.00A5.B07
SMC Version (system): 1.13f3
Serial Number (system): 4H7050UCWGP

I have put another battery into it that I got from ebay and am wondering if this could be the reason. I just don't remeber this getting so hot so early. My girlfriend has same computer- the other day we started up at the same time and after 15 min. I noticed that my fan already kicked on and I felt the bottom-it was very hot compared to her laptop. I also ayear ago installed an Hitachi 250gig hd 7200rpm-but I don't recall the heat coinciding with that installation. So,my best guess is that this new battery is not right. Any thoughts ?

Is it the exact same battery model as originally came with the laptop?

To the OP:

Not all batteries are created equal. Unless the battery is an approved replacement for the original, it may not exhibit the same charge - discharge characteristics as the Apple battery. That may cause overheating of the battery and may also lead to damage of the charger circuitry.

It's very tempting to purchase a battery from eBay or some other third party distributor because it most cases you can save considerable dollars. However, most of those "cheaper" batteries being sold will wear out faster and can may lead to problems.

Solution? Replace with a genuine Apple battery or an Apple approved replacement.

Regards.