You can not use this engine in a C337 as is. If you look at the type certificate it says (using C337 or C337A for example):
Engines (Front) Continental IO-360-C or -G or -CB or -GB
(Rear) Continental IO-360-D or -C or -G or -DB or -CB or -GB
Check the type certificate for your specific aircraft.
C337 type certificate
Here is the type certificate and data on the IO360:
IO360 type certificate
Here is some history on the io360:
http://en.wikipedia.org/wiki/Continental_IO-360
IO360 tc says:
The Model IO-360-D is similar to IO-360-A except for rating and oil cooled pistons.
I'm pretty sure the pistons are oil cooled by oil being sprayed on to them via a spray nozzle which is part of the engine case. So it would be a big deal to modify this.
I've attached a picture that shows the nozzles in the crankcase. Hope this helps.