Why does unsweetened tea get colder, faster than sweet tea?

TL;DR = The sweet tea takes longer to cool down because there is a lot more stuff in it to get cold.

When cooling unsweetened tea, you are cooling almost pure water (the tea solids are negligible). A 12 ounce glass of unsweetened tea has about, you guessed it, 12 oz (by weight) of liquid to cool, or 340 grams (mass).

Southern-style sweet tea (if this is the "sweet tea" you are referring to), has a 2:1 ratio (by volume) of tea to sugar. A 12 ounce glass of sweet tea has 12 oz (by weight) of tea, and 5-6 ounces of sugar (by weight - 8 oz of sugar by volume = ~7 oz by weight). This puts the total weight of the beverage at 18 ounces or 510 grams (by mass).

The sweet tea, in this example, has 50% MORE mass than the unsweetened tea! This extra mass will take more time to cool down, because there is a lot more STUFF to get cold. It occupies the same volume, but there are a LOT more molecules to chill.

Compounding factors:

• Heat Capacity vs. Specific Heat: A detail to this is that a solution of sugar and water has a lower specific heat (by MASS unit) than pure water, so the total heat capacity of the sweet tea is not quite 150% of the heat capacity of the unsweetened tea, but somewhere between 100% and 150%. Intuition would put it somewhere in the 130%-140% range. Read the physics.SE question linked above for some details on that calculation. Rest assured, however, that the heat capacity of the sucrose solution is higher than pure water.
• Conductivity: I've ignored the thermal conductivity of the solution, since I'm assuming that the stirring in the tea makes the small conductivity differences between the solutions negligible, but that calculation could be done as well.
• Convection: Unstirred sweet tea will experience less convection than unstirred unsweetened tea. In the unstirred sweet tea, dense sucrose solution will remain at the bottom while the cold water from the melting ice will sit on the surface (you can actually see this visually if the tea is sufficiently colored). This slows cooling by slowing the mixing of the cold liquid with the warm liquid. In unsweetened tea the cool liquid will sink the bottom, promoting convection and self-mixing. However, convection is a side-issue to the primary point, the total heat capacity of the beverage.

And as a final note, explanations like this really make it obvious how annoying it is that US measurements use ounces for both volume AND weight.

Ice will actually cool a hot beverage faster than a cold beverage. There's two things happening here.

1. The ice is absorbing heat from the water, cooling it through conduction (contact) and convection (flow)
2. The ice is melting, absorbing HUGE amounts of heat to overcome the Latent Heat of Fusion (i.e. Break the crystal structure of ice). This melting of ice and the related absorption of energy is the single largest factor in cooling a drink.

When you put the ice in a hotter beverage, the ice melts faster, and this heat of fusion cools your drink faster.

When you put ice in unsweetened tea, it's temperature is near 100 degrees C, and it will start the ice melting very quickly. When you add sugar to tea, it will cool it immediately. It takes energy to break the crystal structure, and this has to come from the tea, thus reducing the temperature by a small, but significant amount.

This lower temperature doesn't cause the ice to melt as quickly, slowing down the cooling process.

Of course, over a long enough time frame, everything approaches room temperature.

Also, the rate of heat transfer (flux) is driven by the difference in temperature between Hot and Cold. The greater the difference in temperature, the faster heat flows.

My answer is similar to @SamLey, in that we agree the cause is the higher density of sugar solution water. But I have a slightly different take. TL;DR Convection is reduced in a denser solution, so the cold water surrounding the ice isn't carried away as quickly and the ice melts more slowly.

All the data i've found shows that sucrose solutions have a lower specific heat than pure water so one would expect it to cool more quickly. (But who knows how the actual tea components affect it.)

I think the effect you're seeing is due to the density of the sucrose solution.

Ignoring the tea components, a sucrose solution is more dense than a pure water solution. As the ice cube melts in a pure water solution, the cooling water surrounding the cube sinks to the bottom of the glass and the warmer water at the bottom rises, therefore there is increased heat transfer as the warmer water breaks the bonds in the ice more quickly.

But in the sugar solution, the denser water stays at the bottom of the glass and doesn't rise at all. Without any convection currents to carry the cold water away from the ice cube, it melts much more slowly. Also note this effect is compounded by the fact that the melting ice is making the solution less concentrated near the top, so it is even less dense around the ice as it melts.

Since the denser, warmer water stays at the bottom of the glass, naturally it seems to you that the tea is cooling more slowly. This agrees with your observation that if you move the straw to the middle of the ice, the temperature gradient feels a lot greater than in the unsweetened tea.

EDIT: Experiment?

An interesting experiment would be to use a thermometer to measure the temperature after a fixed time of the unsweetened and sweetened tea with ice without any stirring, and then perform the experiment a second time stirring every 30s or so. I would guess that the constantly agitated sweet tea will cool faster than the unsweetened tea, but the undisturbed sweet tea will cool more slowly than the unsweetened tea.