Yes, that's true, and if they're left unaided in the disposal of excess heat, they go into thermal shutdown, which can be frustrating. However, back in the '70's, it was not at all unusual to see a circuit board seriously discolored on the side opposite a 7805. They still regulate when they're hot, so long as the limit isn't exceeded. If one manages the dissipation by means of a series resistor on the input, which is quite simple, and which is recommended in one of the many app-notes, which, back then, were generally quite correct and reliable, one can avoid the trouble. Linear regulators like to have a series resistor at the input anyway, though I prefer to put them upstream of the primary filter cap, since that protects the rectifier diodes, too. It doesn't save any heat, but it helps the regulator.

I also like to use a preregulator, as one might if building an amplifier with a bipolar 30 volt raw supply, since 30 volts is a mite generous for a 7805. The TO3 package, the largest, only is able to dissipate 80W. I try to limit the input on a naked 5-volt regulator to, at most, 12 volts. Heatsinks will help, but not as much as a preregulator to a more manageable voltage.

RE