First, where do these beams come from? From the mosque structure itself. They were removed during renovations.
The beams had been used in the roof structure of the mosque, and already at that time they were said to be thousands of years old by archaeologists preserved only because they had been used in the building.
But the mosque is not thousands of years old. Given that when the mosque was made, the Temple had been destroyed centuries previous, the Arabs would have been unable to use building materials from the vanished first Temple. All the structures on Temple Mount were destroyed after the reign of Roman Emperor Julian the Apostate, but their remains were there - remains of the Second Temple, the Churches and the Roman Temples which were on the site in the early Christian era.
Some of the beams were dated to the first Temple period
They cannot have been, because no archaeologist has ever claimed to have found a single artifact of that era. The search is still on.
others to Roman times, and at least one beam was found to have Byzantine-era designs etched on it.
These sound like beams from the early Christian era.
So - what is happening to them?
After the beams were removed from the mosque, they were stored in a museum on the Mount. However, in recent years the beams were moved to a corner of the Mount, open to the elements and archaeologists fear that exposure to winter rain and summer sun will be their undoing. Some of the beams were taken out several years ago, and more have been spotted in recent months. Reports said that the Arabs, who have been trying for years to ger rid of the beams, have begun burning them.
Reports may say that, but it is not real evidence.
Now, many of the beams have been placed at what appears to be a dumping ground ... Jewish groups that visited the Mount saw the beams being moved, but reported that the Arabs forbade them to take photos of the activity.
This seems like vague hearsay. But if the historical beams (which no doubt have nothing to do with First Temple) have been removed to a dumping ground, then obviously, anyone can sneak in, and grab some of them. Or grab all of them.
I sure am glad you are here to straighten out them silly ignorant Jews in Israel! what do they know?
Maybe they are just burning the beams from their own eyes.
Motes don’t burn well.