"cooler" could mean slightly, marginally, negligibly cooler. So yes, higher voltage typically would result in high efficiency in general, therefore "cooler" for a lot of devices that use electricity, but for audio power amplifiers, higher power supply voltage is for the transformer primary (the h.v. side) only. The secondary (l.v. side) voltage, where the amplifier is connected to, would be the same so the difference in terms of transformer efficiency would be very negligible as transformers are very efficient in general >>90% typically, to begin with.