I have a pc with a dual core 670 processor in an old pc.
Quite similar to yours.
I started up a test using the cpu-Z stress test tab and measuring with HWmonitor.
It uses a stock intel cooler in a fanless case(lian-li PC-Q02)
Initially my cpu temperature was 38c. and the fan speed was 956 rpm.
In time, the processor has heated up to 75c. and the fan speed has increased to 3214.
It is normal for one core to run hotter. My second was at 72c.
First of all, with a normal 22c. ambient, 57c. indicated a cooler issue.
Do a double check to see that the cooler is not loose.
Look at the back of the motherboard and see that all 4 push pins are fully through the motherboard and locked.
It is easy to dislodge the cooler which would explain the change.
Because you worked well before, I doubt that it is any bios issue.
Perhaps more of a problem is why the cooler fan speed has not increased.
Is the fan connected to the cpu fan header?
That is the one which is automatically controlled.
In the bios is there a fan setting section?
It should be set to increase the rpm as the cpu temperature rises.
I do not know what the internal and remote readings are.
There are a couple of different versions of the intel stock cooler.
One will have a more efficient copper bottom.
Others are taller with more heat dissipation area.
A possibility is that the fan is defective.
You should be able to buy a replacement cooler with a copper bottom on ebay for about $12.
Here is an example:
https://www.ebay.com/itm/Intel-OEM-...001617?hash=item2cd10f4bd1:g:ViIAAOSwTQtaSqr8