I'm thinking you're hearing an exhaust leak, especially if it's a 351M or 400. This would explain both qualifiers: under load and cold engine, as many leaks will seal up with heat.
Check, of course, your manifold gaskets and the flanges at the end of the manifolds. If equipped with air injection, check the air pipes, especially the rear cylinder head mounting gaskets, or even the pipe, check valves and hoses.
Also check the EFE valve down at manifold outlet. I forget what side it's on on those models, but it'll be sandwiched between the exhaust manifold and the exhaust pipe, with a vacuum diaphragm coming off of it. Has a valve in there that is only commanded closed when vacuum is provided through a thermal switch. That would explain why it goes away when it's warm too. It could just be flopping around.
EDIT:
A mechanics stethoscope is a cheap investment, and very handy for finding things like this. You would actually pull the probe out of the hose and just listen through the hose itself. Have an assistant rev it up for you when it's cold so you can find it easier.
Another EDIT:
If you do get yourself a mechanics stethoscope, pick up a two or three foot section of 5/16 steel fuel line. You can even bend the end of it a little bit, put the straight end into your stethoscope hose and have a heck of a lot more range and less chance of burning up your hose when you're listening to exhaust components.