I oiled a 15 Clone yesterday - it would not turn for a few hours. Mine had all the usual places baptized with oil. There are places where dried up oil hides and until you get to it you just can't move the machine. After I figured out the stupid thing was reluctant to turn I turned the machine upside down and reoiled. I turned it every direction I could think of and tried to rock it just a little until it turned. Then I oiled and turned again. The idea of it only turning with heat is because you have dried gummy oil somewhere. You are headed in the right direction as far as I can tell. Just don't force it. Gentle rocking and oiling and time... I must have neglected to oil behind the horizontal arm in the front or else oil just didn't get oil in there. I kept thinking the back end by the hand wheel was what was stuck. It was when I focused on the nose end behind all the stuff you can see that it finally moved. What I don't like about Kroil is you have to be sure to get oil on things so it doesn't make rust. Tri-flow or even sewing machine oil and time will usually get things moving. Some times people use 3 in 1 oil and when that stuff sets up it is like chewing goat meat. It just keeps going....
I had one machine that had a broken needle point stuck some place. Once the broken tip fell out the machine moved just fine.
Then a while ago I had a stuck Kenmore 15 clone. I worked and worked on that machine. The needle bar was stuck. In the end I got a hammer and pried it out. When I went to put it back in I figured out that the needle shafts didn't line up. The needle was binding. That machine, too looked like new. No amount of heat made that one turn. In fact the only time it turned was with the needle bar out of the machine. I have a really nice parts machine that I have a LOT of time and effort into and maybe some colorful language............
What ever is causing it will be teaching you a lot.