Nominal operating temperature of CPU

We have started development using the iMX8 and have found the CPU package to be quite warm to the touch.

With an ambient temperature of 72F, the package measures 130F after the startup is complete and running with idle processes using Torizon Core. This is concerning, as the expected deployment will require much higher temperatures, and it is already more than 58F above ambient.

Is this normal nominal operating temperature? Is cooling recommended?

According to NXP datasheet maximum allowed junction temperature is 105C.
You can check it using sysfs interface.

In case of overheating an OS automatically throttle down CPU speed and the shutdown a system if temperature goes above critical. .

Please check this article about Thermal Management.