New evidence for the Arkenstone-Silmaril case

[Sophia the Thunder Mistress]

This is one thing I thought of that speaks against Arkenstone=Silmaril. The hallowing of Varda:

And Varda hallowed the Silmarils, so that thereafter no mortal flesh, nor hands unclean, nor anything of evil might touch them, but it was scorched and withered; and Mandos foretold that the fates of Arda, earth, sea, and air, lay locked within them.

Now in Beren and Luthien's tale, it is specifically said that the Silmaril didn't burn him:

As he closed it in his hand, the radience welled through his living flesh, and his hand became as a shining lamp; but the jewel suffered his touch and hurt him not.

Nowhere in the Hobbit is it mentioned that the Arkenstone was hot, that it burned any of the Mortals who touched it (Bilbo, Thorin, the dwarves who buried Thorin). If it was a Silmaril it surely would have burned, wouldn't it? Something like a hallowing by Varda doesn't wear off.

Sophia