Your thermal calcs aren’t quite right. The formula you have would be correct if the LED was rated for operation in free space, then the datasheet would spec a ƟJA value. But it specs a ƟJC (junction-case) value. There is no spec for a ƟJA so this implies it must be heat-sink mounted.
The correct formulae are therefore :
Tj = Ta + (Ɵjc + Ɵh)×(Pd)
Tc = Tj - Ɵjc x Pd
Ɵjc = junction-case thermal resistance
Ɵh = heat-sink thermal resistance; and
Ta = ambient air temperature around the heat-sink
Tc = case temperature at the thermal pad
This device MUST be run on a heat-sink. By way of examples:
A 40mm x 40mm x 1mm flat aluminium plate mounted vertically in free still air has a thermal resistance of about 46°C/W which would give a junction temperature of 135°C at 25°C ambient (and a case temperature about 10°C lower at 125°C).
A 25mm square, single sided, 25 micron thick, copper area on a PCB as a heat-sink, mounted horizontally and radiating from the top surface only is about 245°C/W and would allow a maximum wattage of 0.45W (140mA approx) for the same temperatures.
Note also that the 700mA limit for the lower spec LUXEON F PC Amber LED is an absolute maximum. From the data sheet you shouldn’t normally operate it above 350mA and 80°C case temperature to avoid reduced life span/premature failure.
Good heat-sink design is a fine art! Hope this helps a bit.
You might also find this site useful: Heat-sink calculator