Mid-2014 MBP Running Hot After New Battery

You can boot into Recovery Mode (Command + R) to access the installer for the current OS on the SSD.

You can also boot into Internet Recovery Mode (Command + Option + Shift + R) to access the online installer for the original OS which shipped with the laptop from the factory or you can boot to the most recent online OS installer using Command + Option + R to access the macOS 11.1 Big Sur installer.

You can also create a bootable macOS USB installer for macOS 10.11 to 10.15 using the instructions in this Apple article:

https://support.apple.com/en-us/HT201372

All of these methods will allow you to install macOS to an external USB drive once the external drive is properly erased (partitioned & formatted).

I don't see anything with the software itself, but I'm not a Mac software expert so maybe another contributor will be able to comment on the software. You do have a lot of stuff I'm not familiar with including lots of browser add-ons. Google Chrome is known to use lots of memory and CPU cycles which can make a computer run hot. Make sure your third party apps are all up to date especially your Wacom Tablet driver.

Adobe is dropping support for Flash at the end of the year so you should uninstall Flash by following Adobe's instructions.

If you downloaded and installed the Canon software, then I would start by uninstalling the Canon software. If this is for a printer, then make sure to first delete the printer from the Printer System Preferences. After uninstalling the drivers re-add the Canon printer by allow macOS to install the drivers on its own (no need to download any printer driver from Canon). If the Canon software is for another type of device, then download the most recent driver from Canon and reinstall it.

If this doesn't work, then run Disk Utility First Aid on the SSD (even better run it on the Container). Even if First Aid reports everything as "Ok" click on "Show Details" to see if there are any unfixed errors listed. If there are unfixed errors then it will require erasing the whole physical drive before restoring from a backup or clone. Recent versions of Disk Utility hide the physical drive & Container from view so you need to click on "View" within Disk Utility and select "Show All Devices" so that the physical drive and Container appears on the left pane of Disk Utility.

If you still have problems, then try reinstalling macOS Mojave over top of itself which should not affect your data or apps.

You can also install macOS Mojave to an external USB3 drive which may save you from having to risk your internal drive.

Run Macs Fan Control and show a screenshot while the system is sitting idle. Take another screenshot of the temps & fan speeds when you feel the laptop is running hot (tell us what apps you are using at the time for some context). If you don't provide your admin password when launching MacsFanControl, then it won't install its driver (just click cancel when it reminds you that you won't be able to control the fan speed).

To look for possible software issues contributing to the Mac running hot you can run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper.