The last couple of sentences of the Variable enhancement description on page 39 address this:
With the Narrator’s permission, the player may even declare the source of the effect is variable as well- for instance a gadgeteering crime-fighter who uses a variety of boomerangs might have an ice boomerang and a fire boomerang. Varying the source of the effect normally only occurs in the case of gadgets or magic.
So it requires Narrator's approval, and recommends (but not requires!) that it happen normally for gadgets and magic.
The '80's version of Marvel Universe's Captain Marvel had the ability to change her body into electromagnetic energy - she could become heat, laser, x-rays, etc. That would be a great example of someone who isn't using magic or gadgets but has her narrator's approval to swap the energy type.
There are a few characters who have control over both heat and cold, which would be more examples.
Other than by using plot device special circumstances, like people using the Cosmic Cube, I can't think of any characters who can use ANY descriptor they want, like molten lava one turn, laser beams the next turn, and green radiation from a destroyed alien planet the next turn. So I would not allow that character without good reason, and might require something extra (Omnipotence maybe?)
For myself, I'm happy to allow my players to have a limited selection of appropriate descriptors if they choose Variable and it fits their concept, but most characters do not.
I do allow characters to have melee and ranged versions of the attack. The Haymaker example in the Blaster archetype is one precedent for that, but not the only one. I only have a few more minutes right now before I have to leave so I don't want to look up others, but I can later if people want more. But basically my understanding is that an energy projector with variable could (if appropriate to his concept) use that energy to enhance his punch or whatever. For example, if AslanC allows it, I'd like to do that with Tempest - he uses his kinetic energy power to super-charge his punch (with glowing energy swarming around his fists of course). Another character who's special attack is something inappropriate like an orbital laser cannon that fires down at his mental command couldn't use that to justify making a melee version of his Special Attack, in my opinion.
If the source of the Attack is completely different, like firing ranged energy blasts and then wanting to have the same power also represent awesome Martial Arts training for melee strikes. In that case I'd recommend to my players that they put it in a multipower (for 1 point), allowing them to have two separate Special Attacks that have different concepts.
In my opinion, if you apply the Special Attack to a melee attack, its damage should be based on Brawn, not Mind. I believe the Haymaker example in the Blaster archetype disagrees with that, but I'd argue it is a typo. The rule under Special Attack is pretty clear about which stat is used for no-range vs ranged attacks.
