Since the architecture of the two machines is so radically different I'm going to say "No way!".
Here's what I will say:
"OK “Will and Way” here goes!
So we’re “force changing the logic board from Core Duo to the earliest Core 2 Duo Late 2006.
You’d probably want the 2 GHz board #661 – 4216
Here’s the main incompatibilities:
Battery – looks to be the same size but probably the connection is different.
I/O frame is different so that will need moding.
Heatsink is different so will also require moding.
Fan is different 922 – 7372 to ..7887
Airport Extreme card is different 661 – 3890 to .4058
Top case is different track pad now has a cable
Optical drive is different - we'll ignore that for now.
Inverter cable is the same - whee!
Mike cable is different - OK so no mike for now
LVDS cable is different - This could be a massive problem."
You'll have to do your own research on how to make this work.
Here's the iFixIt site for the Core Duo:
https://www.ifixit.com/Device/MacBook_Core_Duo
and the site for the Core 2 Duo:
https://www.ifixit.com/Device/MacBook_Core_2_Duo
Open them side by side and try to determine the differences.
So for instance look at step 12 in the procedure for logic board removal. The connector between the keyboard and the logic board is very different.
So that will probably mean a new top case/w keyboard.
Step 24 this is why the Airport extreme is different. No BlueTooth in the earlier one.
Connector might be different to the logic board, antenna connectors is most likely the same.
Step 28 - 29 LVDS connector. Looks very similar and if that is true - major problem overcome.
Step 34 Logic board removal - screws look to be in the same spot so also if true - - major problem overcome.
Step 36 - 37 here you can see the difference in the architecture around the CPU and why a simple CPU switch would require reengineering of the logic board!
OK that's about it. You'll have to be very skilled in working with sub level computer components. Don't force anything that will only result in disaster! Some incompatibilities might require both cables and micro soldering to splice the two incompatible cables to each other.