But what's the point then? Gluing them together or placing them next to each other would make for a much nicer final product. Maybe you could use some of the machines used in precision welding but those are designed for metals, so you would most likely need a custom one. In theory you can "melt together" any two objects that can melt but if the final result is completely irrelevant then what's the goal?

Either way, while I wasn't able to find studies that checked thermal stress in any gemstones I strongly suspect the crystals would crack if exposed to temperature gradients required to do that.