If the thermocouple were not warm enough, wouldn't it shut off the pilot flame? I kind of thought that's how water heater controls usually worked, and that's why you have to hold the pilot light knob/button for a spell after first lighting the pilot. I may very well be mistaken, though.
It sounds to me more like a problem with the thermostatic gas control valve, maybe something sticking internally. If it were me, I'd probably chat with the clerk behind the counter at some local appliance repair place or gas company for their opinion given the symptoms.
