I use the part of my hand that's holding a thermometer. A tympanic probe might be +/- 5°C but that's far more accurate than "I think it feels hot".
Maybe a good idea to get a general tenor of the patient's temperature by using the back of your hand, inside of your wrist or your fingers/palm, but I wouldn't go basing any patient treatments off of voodoo, no matter how you do that voodoo so well.
There's a whole lot more of the clinical picture that we're leaving out here. I would expect hyperthermia to have associated reflex tachycardia, flushing, altered mental status, etc. I would also expect that hyperthermia that is the result of an infection to have my patient present with a "toxic" apperance, shivering at room temperature, general malaise, etc. With hypothermic patients, I would expect them to present with peripheral cyanosis, bradycardia, also altered, perhaps if they were septic a more noticable "toxic" apperance than relative hypothermia...
There's more to this than "what part of your body are you using to check your patient's temperature"... I think if you're relying on subjective data for patient treatment or assessment, it's bad medicine.