Very high current very low voltage application

Power supplies from arc welding devices are quite capable of what you describe. You may also try a soldering gun (the kind with a transformer inside) replacing the tip with your stuff.

Just be aware that you need really really thick wires for 100A. The problem will be worse with high frequency AC because of the skin effect.

As far as the regulation is concerned you should be able to use a simple PID regulator with a thyristor output for the soldering gun. The arc welding supplies may be more difficult depending on their internal construction.

How thick is that strip? Aluminium is very reactive and oxidizes instantly when exposed to air, leaving an insulating coating on the aluminium. The resistance of this coating may be much higher than the strip itself, so that the largest part of the power is actually used to heat the contacts, even melt them. Make sure the contact surface is large enough.

No need to wind a transformer, since 1-turn output should work. On ebay find a 120V, 200VA toroid which has an obviously open center (some are epoxy-filled!) The secondary will be unused (can be anything.) Pass a metal bar or even copper pipe through the center. That should easily give you 0.1VAC output on the ends of the pipe.

If it's a bit too low to drive thin foil, you might need to use two pipes, with outputs connected in series for 0.2VAC output (really it's a 2-turn secondary.)

Very useful is a 100watt Variac on the 120VAC input. That lets you adjust the input voltage between 0% and 140%, for net load wattage 0% to 200%.

For general reference, here's measured values on the transformer in a typical (Radio Shack) 230watt soldering gun: secondary is 5 turns, the AC output is 1.0V unloaded, falling to 0.6V with a 200W load (soldering tip.) That's 0.1 - 0.2VAC output for each single turn in the secondary. (This is typical for the power transformers I've measured in the past.) Clamp-on meter says the soldering-tip current is over 250 amps.

Note that the output current starts dropping as soon as the load conductor heats up.

Also: To avoid the problem with soldering to aluminum, I'd also try copper foil, or for higher ohms, some thin brass sheet from a hobby store.