How do step-up transformers work?

I think what you're missing is the current...

• Step down transformers change a high voltage/low current, to low voltage/high current.

• Step up transformers change a low voltage/high current, to high voltage/low current.

So, in an ideal 100% efficient transformer, the power doesn't change and no heat will be generated by the transformer, i.e. the power in = the power out, because Power = Volts x Amps.

Think of a transformer as being a like gearbox (or pulley system, or lever, or other such machine). A 10:1 gearbox can turn a 60rpm rotation into 600rpm, but if the output requires a certain amount of torque to rotate, the input will require at least ten times that much (slightly more, in practice, because of friction in the gearbox itself).

Think about it this way: magnetic field have no idea how many loops you have on the second half of transformer.

So, each loop on second side works like a small 'bettery' connected in series, the more loops - the more batteries - the more voltage.

But as there is the same amount of magnetic field is divided on all loops, achivable current is less.

Same works another way: Less loops - less voltage, but more current as more magnetic field is left for 1 loop.

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In ideal situation no heat is generated. Heat is generated the way you say only in linear regulators.