Is it necessary to run some software like CPUIdle/CPUcool to reduce the CPU temporature and do CPU optimization in Sony TRs? I never feel it was too hot though ...

The Pentium-M processor in the TR already has dynamic voltage/speed throttling, and insures that the CPU runs as cool as possible given your power settings. It’s already pretty optimized for battery life and power consumption, with parts of the chip that are put into a sleep state and are woken up only when necessary. With a desktop chip, the programs might be of some benefit, but not on the TR.