Now I see that smartctl can read this data, and hddtemp cannot; so it ought to be fixable:

$ sudo smartctl -A /dev/nvme0
smartctl 7.2 2020-12-30 r5155 [x86_64-linux-5.10.3-arch1-1] (local build)
Copyright (C) 2002-20, Bruce Allen, Christian Franke, www.smartmontools.org

=== START OF SMART DATA SECTION ===
SMART/Health Information (NVMe Log 0x02)
Critical Warning:                   0x00
Temperature:                        49 Celsius
...

$ sudo hddtemp --debug /dev/nvme0
ERROR: /dev/nvme0: can't determine bus type (or this bus type is unknown)

But I want to use the hddtemp daemon for this, to avoid needing to use sudo every time I want to check it.  I generally write a "pow" script for every system that I use, to monitor sensors, fans and power, and "nc localhost 7634" is a good addition to that.