This Ableton tutorial covers two easy-to-overlook sources of CPU drain in Live: oversampling and Complex Warp Modes. Both can quietly inflate your processing load without any obvious signal in the mix.
Oversampling can be active in both native Live devices and third-party plugins. You can toggle it off through the context menu in a device's header, which is worth checking if your CPU is running hot.
Complex and Complex Pro Warp Modes are also expensive to run, especially across multiple clips at once. If you're warping many clips simultaneously and hitting performance limits, consolidating that audio to disk removes the real-time processing cost entirely.