i have a 1966 289 mustang and ive been having this problem where after it is driven for a little while it makes a "puff" noise from the exhaust when under acceleration and it doesnt really change with how hard i push it.ive changed the spark plugs,spark plug wiring,ignition coil,radiator,water pump,thermostat,all hoses,fuel pump,oil,oil filter. over heating isnt a problem,and there is no kind of smoke or anything coming out of the exhaust.

 

Sounds like your running too rich and the unburned fuel ignites in the exhaust.
OR
Exhaust leak, but that's more of a ticking sound.

Someone else will chime in.

 

If you've got the stock exh. manifolds check the 'donut' gaskets between the exh. manifold and downpipe. Some are soft gasket type, I swapped to the all steel ones and cleaned up both surfaces and solved my exh. leak that I could hear. Probably not constant because it was more evident when the cylinder closest to it fired.
Jon