Why do three AA batteries inline get hot?

Does 'rigged' mean they were physically in the flashlight? Sounds like you managed to find a direct short from positive to negative, but it's kind of hard to guess how.

I was attempting to reach 4.5 volts by using a plastic three-AA battery holder from a toy that I wired in line. It's possible it may have made contact with the brass outer body. But still I could use an explanation beyond that.

You shorted the batteries. When you have a short, you get a very high current, energy = voltage * current and energy is expressed as heat. You probably also killed your batteries.

The other explanation is that the 703 battery, aka lantern battery, can deliver 3-4.8 amp/h.

The AA battery, or LR6, can only deliver 0.4-1.8 Amp/h.
If you connect them in series their total current remains the same.

Which means that if your WW1 lantern's consumption is greater than 1.8 amp/h, your AA batteries are going to heat.

A very lucid explanation. Thanks!

My pleasure.