Sounds very much like what happens to me when I've been overexerting myself really badly. One of my specialists believes it to be related to inflammation of my spine and/or brain (the encephalomyelitis part of Myalgic Encephalomyelitis) . Often the skin on my face especially gets feeling really hot, in a very distinctive way, and my whole body gets super weak and shaky, like you described. My skin does tend to actually get overly warm to the touch sometimes when it's happening, but I don't register as having a fever so I think it's probably just extra blood close to the surface of the skin (which makes sense, since I often get visibly flushed). I also often get sweaty when this is happening or about to happen, and sometimes I'll have a concentrated burning along my upper spine and into my head as well if it's bad enough (usually if I try to push on with what I'm doing rather than stopping as soon as I notice the heat).
For me, I've now learned it's a sign that I've done WAY too much (usually mental activities, like watching TV or using the computer or talking with someone - I've gotten a lot better about not overdoing it physically, but mental still gives me trouble sometimes). I find a little bit of relief from drinking lots of cold water and putting an ice pack along my spine and the base of my head. And I definitely need to stop the mental activities entirely for a while to let it calm down some. But once I've gone far enough to trigger the problem it tends to linger around at at least a low level no matter what. Trying to avoid triggering it in the first place has been far more effective, and if I can manage to avoid going too far that way, then the amount I can do without problems seems to gradually improve over time.