Other than during sustained transfers of large amounts of data at continuous maximum speed, being in an enclosure won't be a big issue. In normal usage, with an enclosure that provides any sort of heat dissipation (thermal pad providing contact with the metal enclosure) there just won't be time for the temperature to rise and stay high, and if it happens occasionally it's not a problem. An M.2 SATA drive will have the same issue anyway (and are you sure your enclosure accepts them?). PCIe3 drives also just don't get super hot.
The NVMe controller isn't going to be operating at maximum performance to feed a USB interface so it's not the fact that it's a high-performance chip that's the issue, it's just the limited space for the heat to go. (Even in a mini-PC, there's space on the sides and underside of an SSD where air is flowing and heat can dissipate in addition to the top, which may or may not have a heatsink; there's nowhere for the heat to go in an enclosure except the enclosure surface via the pad. Even having vents in the enclosure doesn't help much as they don't have forced airflow and are often only on one end so there's no "through" flow.) Even during a long ATTO benchmark my PCIe4 drive in an enclosure only gets up to 40C. My internal drives, even with heatsinks, IDLE much higher than that (they don't increase as much during the testing though, and the external drive is exposed to a much colder ambient temp).
As far as not wanting to "ruin hardware for no good reason", at this point it's simply e-waste since it's not being used, so why spend more money NOW buying another drive in order to "preserve" an old drive that is just getting older by the day, and which you may never make use of later? You have the drive in-hand which might just sit in a drawer until it becomes totally obsolete, so use it now for whatever purpose seems good. It's not even like that was an astounding drive to start with (you didn't mention the capacity so I don't know the speed rating), and drives with double the speed can now be had for $60 or less.
A 10Gbps USB enclosure will of course have much lower bandwidth (about 1GBps) than a PCIe3x2 internal connection (2GBps), limited by the drive spec rather than the slot, so even though the drive won't be able to operate at it's maximum PCIe capability, it will be better than the external use when speed is the priority. The USB interface itself introduces other issues like latency, too, and a hit to random performance. If you used a Gen2x2 enclosure with the drive, then you'd have bandwidth more closely matched to the internal slot.
So it really depends on what you think you might want to do with the drive, which somewhat depends on the capacity and what you've got in the system otherwise, and what you might possibly do with it if you used it internally when you've already upgraded your storage. I'd use it as an external backup drive if it has the capacity for all of the data you currently have, otherwise either use it for sticking really unimportant files on that you probably don't need to access often, or use it to upgrade some other machine to extend that system's life. If you use it for backup and your internal storage usage increases later so that the drive is no longer large enough for backups, THEN you'd consider replacing it with a larger one. At that point, SATA is still pointless because there's virtually no cost savings, and there aren't any large M.2 SATA drives anyway, and the heat from performing backups is simply not going to make the drive die any sooner than it would have otherwise. A drive that can max out the 10Gbps USB will also be cheap as chips by then. At worst, it might throttle sometimes, but if it's being used for backup then that isn't really an issue and probably won't happen since backups don't stream the data that fast, and if it's throttling then it's preventing it reaching temperatures that might reduce the lifespan.
What do apps like Crystal DiskInfo show for the health of that drive, anyway? Was it heavily used, bought when it first came out, etc.? After 4 years it's not exactly "young".