Hi Mrpachimari,
Welcome to Apple Support Communities. I understand that after upgrading to macOS Catalina you're seeing "TextInputMenuAgent" and "distnoted" are using a significant amount of CPU which seems to be causing your fans to run and the battery to drain faster. I can see why you'd reach out about this; I'd like to help. If you haven't already, I'd suggest using these steps:
To quit a process, first try quitting it normally. For example, quit Safari by switching to Safari and choosing Safari > Quit Safari.
If you can't quit a process normally, you can use Activity Monitor to force it to quit. Save any documents related to the process, then select the process in Activity Monitor and choose View > Quit Process.
If you don't recognize the name of a process, it might belong to macOS or another process that you do recognize. To see the relationships between processes, choose View > All Processes, Hierarchically. If you see that a process belongs to an app, such as Safari or Mail, quit the app before deciding whether to quit any of its processes.
To help avoid malfunctioning processes, keep your apps, plug-ins, and operating system up to date.
See how apps affect Mac performance, battery runtime, temperature, and fan activity
After quitting both processes, restart your Mac and test again for the behavior; let me know what you find.
Best Regards.