I've had several experiences of oil pressure decreasing with oil temperature rising on piston engines. This has been indicative of engine internal failure with a oil filter full of metal.
Like the previous post says, on the radial pistons there is usually a hell of a lot of oil spewing out of the engine which indicates oil system problems.
I've had a jet engine loose all it's oil on me, but I've chopped it before oil pressure and temperature became an issue as the quantity gauge was dropping off during the ground run. Made a bit of a mess.