The heat produced by a voltage regulator isn't a function of the voltage, it's a function of the power.
You can calculate the power the voltage reg will dissipate by taking the voltage-drop across the regulator, times the current flowing through the regulator.
E.G: $$Power = Volts * Amps$$
In other words, if you have a 30V source, and your device is running off 3V, you have \$30V - 3V = 27V\$ across the regulator. However, if your device is only drawing ~3 mA:
$$27V * 0.003A = 0.081W$$
You would only have a dissipation of 81 milli-watts, which wouldn't even get too warm to the touch.
However, if you have a 5V input, with a 3V output (giving 2V across the regulator), yet your deice is drawing 1A, you have:
$$2V * 1A = 2W$$
You have a power dissipation of 2 watts!
Basically, there is more involved in evaluating heat production then just the voltages
No. There has to be some reference. IF you find a standalone current sink part, it has the reference built in.
The LM10 is a good choice for your circuit: it has a low-voltage reference built-in, and it will work over a wide supply range.
A modern alternative to LM10 is TL103 or TSM102.
Best Answer
The primary reference is something like a zener diode or a band-gap reference or maybe a floating gate MOSFET. The regulator is something like a power amplifier that provides an output that is proportional to that voltage. The gain of that amplifier determines how much the output voltage changes with load current changes (load regulation).
Although the reference can operate okay from unregulated input, there will be some change with input voltage (line regulation). To improve that regulation we can start up the reference in some way and run it mostly from a voltage or current related to the output voltage. This is called "bootstrapping".
Here is the block diagram of an MC78M05 showing the basic regulator and protection circuitry.
Here is how the schematic of an LM7805 breaks down:
The green part is the startup circuitry. The yellow is the bandgap reference. The rest is the error amplifier, feedback divider and protection circuitry.