Yes, the IDs in the default skin need to be updated to match your hardware. Please edit the "Documents\Rainmeter\Skins\HWiNFO\@Resources\HWiNFO.inc" file to update the IDs.
You have the DTS Core 0 temp selected in the picture of the shared memory viewer. So in your instance, you can edit the file to put in these:
; CPU 0 DTS
Save the HWiNFO.inc file, and refresh the skin. Your Core 0 temp will now show in the CPU temp section. You should use the "Core Max" ID instead of Core 0, but as you don't have it selected I'm not sure what you have in there as a value.
The default skin is actually the "Documents\Rainmeter\Skins\HWiNFO\HWiNFO.ini" file. I broke out all the variables into a separate file so it was easier to edit - you don't need to navigate through the skin code.
So in the skin, this code is what creates the CPU temp measure:
If you were to remove the variables from the second file and just insert them into the skin directly without using variables, the code would end up:
You can just do this if its easier and you are not distributing the skin. If you are distributing it, I'd leave all the variables in a separate file like I did in the demo skin to make it easy for users to update.
Hope this helped. Let me know if not.