I've experienced something similar today. I've checked my Orange Pi Zero (256MB) v1.4 numerous times over the past few days, and it's seems to follow a consistent pattern of working its way up to 58/59 degrees C over the first 10-15 mins, after which it remains at that temperature. It's simply idling, not running any programs at the moment.
I then added on the expansion board with the 2 USB ports, and the temperate went up to 63 deg. C, and stayed there.
I was using a power supply with 2 USB outlets, which (allegedly) outputs 2.1 amps total across the 2 outlets. It was powering the Orange Pi Zero and a Banana Pi. Having read the above, I tried powering the OPi Zero (with expansion board) separately with a Raspberry Pi Charger I had handy (5V and 2.5A, I think, and probably better regulated), and the temperature levelled out at around 53 deg C - so a drop of 9-10 degrees.
System info:
ARMBIAN 5.38 stable Ubuntu 16.04.4 LTS 3.4.113-sun8i
System load: 0.03 0.03 0.05 Up time: 9:05 hours
Memory usage: 12 % of 241MB IP: 192.168.1.163
CPU temp: 53°C
Usage of /: 9% of 15G
Output from Armbianmonitor -m after changing power supply:
Time CPU load %cpu %sys %usr %nice %io %irq CPU C.St.
07:44:36: 240MHz 0.05 1% 1% 0% 0% 0% 0% 53°C 0/7
07:44:41: 240MHz 0.04 1% 1% 0% 0% 0% 0% 53°C 0/7
07:44:47: 240MHz 0.04 1% 0% 0% 0% 0% 0% 53°C 0/7
07:44:52: 240MHz 0.04 1% 1% 0% 0% 0% 0% 52°C 0/7
07:44:57: 240MHz 0.03 1% 1% 0% 0% 0% 0% 52°C 0/7
07:45:02: 240MHz 0.03 3% 1% 1% 0% 0% 0% 54°C 0/7
07:45:08: 240MHz 0.03 2% 1% 0% 0% 0% 0% 52°C 0/7
EDIT:
I thought I'd spoken too soon, as after running for around 10 hours at 53 deg C, the temperature climbed to 63 over 10-15 minutes. But an hour or so later it was back down to 53. Not sure what that was about.
I managed to lower it by another 5 degrees, to 48 deg C, by simply standing up the OPi Zero (with expansion board) vertically, on the edge with the pins (which is quite easy to do when it has the expansion board on it). Previously it was sitting flat on a piece of wood, so very little ventilation to the underside.
Allegedly it should be fine up to 70 or 80 deg C, so 48 deg C doesn't seem TOO bad - although that's at idle, with no case, on edge; and sitting next to this OPi Zero is my Banana Pi working as an Openmediavault NAS (with pretty infrequent activity), running at a cool 34 deg.
2ND EDIT:
Still a bit unpredictable. I booted up my OPi Zero last night and monitored it all night. No case, stood on edge, and just idling. Within 10-15 mins the CPU temp went up to around 57 deg C, and it stayed at that temp all night. This morning I simply rebooted it, without waiting for it to cool down. It went up to 47/48 deg C (only took a couple of mins, as it was already warm) and it's stayed at 47/48 for 4 hours.
