as the topic asks: is there a temperature sensor on the board and could we access it?
I would like to roughly check the temperature inside the box the Nextion is mounted on, but rather would not add another sensor to it.
The short answer is No. There exists no such sensor access.
Off the top of my head, I do not recall having run across a temperature device reading for the Cortex-M series M0 or M1 MCUs which are employed for the Nextions. This could be discovered in the STM/GD documentation for the chip on the back of the Nextion ie: STM32F030C8T6 - go to www.st.com
I would highly doubt that even if it existed, it would be brought forward in the firmware implementations.