Ok. You're never going to believe this one. The Fire Stone works EXACTLY like the Lump of Ice, the only difference is that it gets effect #1 of the Lump of Ice in November, December, and January instead of May, June, and July.
So what happens when you have the Fire Stone AND the Lump of Ice? It's like having 2 Lumps of Ice or 2 Fire Stones: the Rest bonus is not increased one bit.
This is more info released by Nevistar. For info on the Lump of Ice, refer to the thread "What does the Lump of Ice do?"