...Doe Firefox also show high CPU if you close Firefox? If so, then I would certainly follow the steps provided by JPBill above and if that doesn't help, try uninstalling, then reinstalling FF.
Another possibility would be malware.. If you haven't use the Malwarebytes scanner, please try using the instructions below to run a scan with the free tool listed:
Please download Malwarebytes' Anti-Malware from the link below:
Double Click mbam-setup.exe to install the application.
* Make sure a checkmark is placed next to Update Malwarebytes' Anti-Malware and Launch Malwarebytes' Anti-Malware, then click Finish.
* If an update is found, it will download and install the latest version.
* Once the program has loaded, select "Perform Quick Scan", then click Scan.
* The scan may take some time to finish,so please be patient.
* When the scan is complete, click OK, then Show Results to view the results.
* Make sure that everything is checked, and click Remove Selected.
* When disinfection is completed, a log will open in Notepad and you may be prompted to Restart.
* The log is automatically saved by MBAM and can be viewed by clicking the Logs tab in MBAM.
If MBAM encounters a file that is difficult to remove,you will be presented with 1 of 2 prompts,click OK to either and let MBAM proceed with the disinfection process,if asked to restart the computer,please do so immediately.
Hope this helps.