Let's put it this way... Something is causing a very deep knock or "thud". How it might be connected to temps is unknown and needs to be determined. The frequency of the knock tends to point to one cylinder which, in turn, leads toward the parts within that cylinder.
Since this knock seems to be related to engine rotation and seems to disappear as the engine warms, I'd have to agree that a faulty rod or pin would not "heal" itself. Usually I'd expect the opposite. Further, I'd somewhat expect that by now you'd have a new window in the block or at minimum some large metallic pieces in the oil pan. So we've got what appears a rotational knock in colder conditions which disappears as the engine warms. The engine hasn't shed any internal components and seems normal as far as operation and power.
Your valve train runs at half the speed of your crank so it rotates at just about seven times a second at an 800 rpm idle. Actually slow enough to count. Bottom end "knock" willl be at twice that rate for a bad component such as a rod or pin.
Once we determine the frequency of the knock we can begin to determine its cause. If directly related 1:1 with crankshaft speed, then it has to be the bottom end and has to be somewhere between the accessory pulley and the flywheel. Given that temps seem to be in play and that the engine is still in one piece I might begin to suspect a failed DMF if this be the case. "MIGHT", but I don't think so.
Should the frequency be 1:2 with reference to the crank speed, then you have a top end problem. Since dry lifters in my experience at worst only make an annoying "tap" until they pump up, I doubt a lifter problem. And since the knock subsides with temp and top end timing is hard set, I'm having a difficult time believing a mechanical problem with rotational components there. Of course it might be possible that you have a valve hanging in its guide and being returned by virtue of "help" from the associated piston. Since our valves are vertical in relation to the piston there's little chance of actually bending a valve but you'd certainly get a knock. Obviously this would indicate a serious problem between the valve and lifter. Very likely an immediate reason to pull the head.
Then the wildcard as far as I'm concerned... Injector problems. In theory it's possible for an injector to introduce fuel into the cylinder at some point well before it should. In this case and because your glow plug will be hot, it's possible to have ignition far before the normal timed event. This would certainly cause a deep knock as the piston would be driven in the reverse direction to engine rotation.
As I consider what I've shared I'm beginning to place the mechanical problems somewhat aside. If pre ignition or better said pre injection actually be the problem and associated with colder conditions, then I'd say glow plugs may be the key. They allow ignition without the heat of compression. As the engine gains heat, then compression takes over the ignition process. In your case a gross pre injection event would cause quite a rattle when cold but subside as things warmed. The timing and ignition of the affected cylinder would still be uncontrolled, but masked when hot. In other words similar to a runaway but not so due to the fact that fueling is still controlled.
So after hearing what I was sure was a rod knock... I think it is! Sort of anyway. Now I'm leaning toward a faulty injection event causing what those in the gasoline world think of as a pre ignition knock.
No matter though. A deep knock in any engine is cause for concern. It's not normal and it's a sign of a potentially serious issue. It can't be ignored.