Because my Radeon HD 5400 card is getting too hot, I want to fall back on the Intel card. How do I do this?
Some computers have a hidden advanced BIOS configuration mode. On my HP dm4t this is accessed by pressing "A" immediately after or at the same time with "F10" (used to enter BIOS setup).
Depending on the manufacturer and bios model and available updates it might be possible to change the GPU mode from Hybrid, to integrated GPU (iGPU), discrete GPU (dGPU). If this option is enabled (and working) in your case, it will turn of the card that is not selected and Ubuntu will work as if you have only one card.
On my HP dm4t only Hybrid and iGPU options work, dGPU will freeze the laptop when saving changes in BIOS.