I have found that allowing them to sit vertically against my chest works well, and I wrap my middle finger and my thumb gently around the throat under the jaw so they can't wriggle around too much, but be very careful not to strangle your little one! As for getting them to take the meds I usually put drops on the bottom lips until it is gone. They will lick the medicine off their lips and that way I don't end up giving it too fast. I also found another way to hold them that works fairly well, with the body resting in the palm of my hand, with my index finger and middle finger curled up on either side of the body in front of the shoulder blades. This again helps control the movement of the head. I have found that wrapping them really scares and stresses them, and also causes them to get overheated, as you said. I think it's just a matter of experimentation and finding what works for your chin.
Also, I have found that pretty much all of my chins hate critical care with a passion, but if I grind it up with a small amount of papaya, hay, and add a small amount of grape pedialyte and a drop of honey, they suck that right down. Again, I think it's a matter of experimentation and finding what your chin will take.
I hope I was able to help.
Good luck!