No. Intoxication is generally considered to be mental impairment or a change of mental state, like mood, inhibition, etc. The warming feeling you get from alcohol is due to alcohol dilating blood vessels, moving more warm blood to your extremities and skin. It is a real physical reaction, not a mental perception. So while you might also be intoxicated, the warm feeling is not intoxication per se.
Well, no. It is a drug and drugs do different things to different systems at different levels. You can't just assert that a drug must be doing B because it is doing A at the exact same dosage.
