Recommendations for replacing time capsule

I have a combo router/modem via Xfinity (see attached photo). So would I just need to get, say, an external hard drive to transfer the documents/files/photos I have stored on my Time Capsule to for storage?

If you are asking if you can connect a USB drive to Xfinity modem/router and use it for Time Machine backups.....the answer would be "no".

There are only a very few routers that will support Time Machine backups......among them are the upper end Asus routers and the Synology router.

No other manufacturer offers a router with a "built in" hard drive the way the Time Capsule has been designed. So, if you opt for another router and hard drive, you will have at minimum two devices to replace the Time Capsule not one.

If you don't need another router, then a Synology NAS would be worth a long look.

My Time Capsule is several years old. I keep getting the flashing light indicating it is overheating, and nothing I do fixes that.

You did not indicate what you might have done to fix the "overheating" issue and whether you have already tried unchecking the box in AirPort Utility for the Time Capsule to "Enable file sharing".

We ask this because there is a bug with the Time Capsule which produces a false reading of overheating when nothing is really wrong with the Time Capsule.

Is the Time Capsule hot or warm to the touch? If it's not, the Time Capsule may not really be overheating, so you might want to investigate this a bit further........before......you look for a replacement for the Time Capsule. Post back if you want to look into this possibility.

Normally, you can expect about 5 years of use from a Time Capsule before it may begin to start acting up.

What have people replaced their Time Capsules with as their Time Capsules have worn out or stopped functioning?

Synology NAS.

Or a suitable router that supports Time Machine to a USB drive.. eg Synology Router or high end Asus.

Bob's fix of turning off file sharing will stop the TC working as a backup device.. so if turning off file sharing does work.. you should be able to go into the airport utility disk tab and turn it straight back on.. it is the cycling of a setting that fixes the issue NOT a fault in file sharing that causes overheating.. just to be clear.