biggs, I think we're getting some confusion since the circuit essentially requires two voltages to operate. On the Vin pin, it requires 5 volts. This is the IC's operating supply that it uses to power it's internal circuits. This supply should have very very little current flowing on it. The other supply is the +LED voltage, which is applied to the positive end of your LED string. The LEDs drop "most" of that voltage and the remainder is applied to the LED pin. The IC must dissipate this entire voltage at the LED's current, which is where the potential for heat and waste comes from.
So, the difference between our circuits and yours might be in the voltage "left over" after the LEDs have dropped your supply voltage, i.e. the voltage sinked at the LED pin.
Can you tell us your input voltage for the LED string? i.e. your supply voltage? Also, the total Vf for your LED string (guessing it's 3.4 * 5 = 17v)? The difference between those two voltages is what your chip needs to drop.
Can you verify with a known-good multimeter that your LEDs are operating at 700mA?
To operate, the IC needs to be dropping at least .5v on the LED pin. At 700mA, that's .35w, so not very much at all, but I'd still expect it to create more than 2 degrees of temperature rise on the IC.