Upgrade to 64bits
Can a 32bit IMac be upgraded to 64bit or does it require new hardware?
Can a 32bit IMac be upgraded to 64bit or does it require new hardware?
No. A 32 bit iMac has internal hardware that limits it to 32 bit so it is not able to be upgraded to 64 bit.
If you have a Core Duo processor you have a 32-bit CPU. It wouldn't be worth replacing the CPU.
Upgrade to 64bits