My shower has 3 knobs & the spout. The diverter (that turns from spout to shower) is in center of shower wall between hot & cold knobs. I've checked to ensure the diverter knob is fully turned onto shower. Is it difficult to fix/replace when the diverter isn't on the tub spout?
If you get warm water out of the spout and cold water out of the shower head, then I sounds like you've isolated the potential problem to the diverter (only other thing that comes to mind is some kind of water pressure based issue, but I can't think of where that would happen on the hot water side only since you have separate hot/cold knobs).
Since this is after the hot/cold knobs, you can probably fix this problem without even shutting off the water, just place something over the drain (don't want to lose a screw), disassemble the diverter, see if it's just an o-ring or dirt, and if not, replace the entire part (take the old one to the hardware store to find an exact match).