What generates heat is not voltage or voltage fluctuation. It is power consumption, also referred to as power dissipation. In the case of an amplifier, the amount of power dissipated at any given instant is equal to the AC power going into the amp minus the power that is delivered to the speakers. Power at any given instant is equal to the product (multiplication) of voltage and current at that instant.
Heatsink temperature is dependent on many variables, in addition to the amount of power that is dissipated. Those variables include the size, weight, and overall design of the heatsink.
The amount of power dissipated by the amplifier is also dependent on a great many variables. One of the most significant variables is its class of operation (A, AB, D, etc.) See this
Wikipedia writeup for further information on amplifier classes.
The best and one of the most powerful amps on the market under $10K is the Sander's Magtech amp.... It has a patented linear voltage regulator that eliminates voltage switching and voltage fluxuation which is typical in most amps which is why they run hot.
I have no knowledge of the Magtech's patented linear voltage regulator, but I don't doubt that the amp is an excellent one. In general, though, a linear regulator will be much less efficient, and dissipate much more power, than a switching power supply rated to provide a similar output.
Amps that are luke warm to slighty warm is a good sign the designer did a good job regulating the voltage.
Not true. As I indicated, there are a great many variables that affect heatsink temperature. In general, voltage regulation has no specific correlation with power consumption or heatsink temperature, and whatever relation might exist could be in either direction depending on the specific design.
Regards,
-- Al