It might go beyond the temperature of the liquid, though: caffeine is a vasoconstrictor, meaning it restricts blood flow to your extremities, meaning you'd be better at retaining your core temperature. (That said, you should also be "feeling" colder in your hands and feet.)
(This is the opposite effect of alcohol, which is a vasodilator: it makes you feel warm by filling your extremities and outer layers with blood, but at the cost of actually losing core temperature. Hence drunk people easily freezing to death in winter.)
Caffeine is generally thought of as a vasodilator. It's a bit more complex than that, but it definitely doesn't restrict blood flow to your extremities.
(This is the opposite effect of alcohol, which is a vasodilator: it makes you feel warm by filling your extremities and outer layers with blood, but at the cost of actually losing core temperature. Hence drunk people easily freezing to death in winter.)