Running out of GPIO & looking for suggestions
Two main solutions comes to my mind:


GPIO expander (as you mentioned). It is really easy to use them as digital inputs or outputs. So you can connect button, LED, transistor and maybe even display (you did not specified type of the display, so I assume standard LCD 1602 or 2004 display). You can also connect SPI-CS signals to the expander, but this depends on used libraries...
Auxiliary Arduino e.g. Nano. Arduino can be used for measurement of the temperature and other stuff and NodeMCU for communication. In this case you have to implement some kind of communication between these two boards (SPI, I2C or UART).