Do I need to add a heatsink to the Hypex amplifiers to cool them?

Yes! Never operate the amplifier without a heatsink or you will risk overheating it. Even the 90% efficient UcD700 running at full power dissipates as much as 70Watts. Simplest solution would be an all-aluminum case to which the amplifier is mounted. When using a steel case a regular aluminum heatsink should be used inside. Make sure there is always some airflow through the case by means of venting holes. Please refer to the "Thermal design" application note for more information.