you must realize that there's very little thermal inertia in the semiconductor die itself, especially if the LED is properly heatsinked (the heatsink should have a lot of thermal inertia). what you should do here is first find out what the semiconductor die is made of. each semiconductor has a characteristic change of Vf per degree C of temperature change. once you know this, you can measure the forward voltage with just enough current to turn the LED on, and the heatsink in a liquid bath (preferably water) at 27 degrees C (this is 300 degrees K. which is one reason this particular temperature is used for so many measurements). if the spec sheet shows any measurements at 25 degrees C you can use 25 degrees for comparison against the spec sheet. so for every degree C of change, the forward voltage of the semiconductor changes. for instance, silicon (nobody makes LEDs from silicon, but it's Vf/T characteristic is well known) has a characteristic temperature coefficient of -2mV/deg C. so if the forward voltage is 0.7V at 25C, at 27C it will be 0.696V. at 40C it would be 0.670V. the same effect is present in all semiconductors, each material with a different coefficient, some positive, some (as in the case of silicon) negative, and there may be some very close to zero. so, once you have established a forward voltage as a starting point, you can either look up the coefficient (assuming it's either in the data sheet, or they tell you what material is used and you can look it up elsewhere) or determine it yourself. to determine it yourself, you use the current source to set a current that lights the LED but produces very little heating. then you change the temperature of the water bath, and for several points (such as at 10 degree increments) plot the temperature and the forward voltage. so you can plot the curve yourself, do some math and arrive at the coefficient. to measure in the manner you're describing, you need a very fast way of switching between sources for the LED, because waiting a second or two while you switch wires, wait for your meter to settle and read the meter, is way too long. it would be best if you could have not only a fast switching method, but a sample-and-hold circuit so that you could very quickly grab the reading and take all the time you want to read it.