I love that you replied with this. I'm going to tear it apart piece by piece.
1) It's disputed whether or not cars still need to be broken in, as modern lubrication and machining have come a very long way from cars of yesteryear. But I'll humor you and just say that, for the purposes of this argument, cars do need to be broken in. However, I'm not sure if you know this, but for a car to operate, there are orders of magnitude more moving parts than there are in a headphone. Large, interconnected, complicated gear systems held together by parts big and small -- compare that to a pair of headphones, where the only moving parts are drivers (and they move very, very little during actual operation. It can be measured in millimeters or less).
Furthermore, your example falls apart because a car's performance does indeed degrade over time. Go ahead and take a 200k mile Ford Focus for a ride and tell me it's as nice as a factory-new model. If the same principle applied to headphones, you would in fact be wearing out your headphones by "burning them in," which goes against the magical performance improvements that you claim.
2) Your anecdotal evidence, in fact, does not mean anything. I, too, own a pair of HD598, and I can certify you 100% for sure that they sound the exact same as they did the moment I took them out of the box three years ago.
3) Headphone drivers are small, even in the biggest of headphones, and the temperature that they generate during operation (even at high volumes) is negligible. It's true that matter behaves differently at different temperatures -- but even if I were to be generous and say that your drivers are a few degrees F warmer after operating for a few hours, paper/biocellulose/carbon fiber/PET/whatever material the diaphragm is made of do not behave in any perceptibly different manner at, say, 85 degrees versus 88 degrees.
4) Furthermore, if the change in sound could be attributed to physical warming of the drivers, they would cool off after not using them, which means that you would constantly need to be "burning them in" before each use. This is preposterous.
5) There isn't really a scientific consensus about whether or not tube amps measure and sound differently after reaching a certain temperature. Certainly, tubes do get quite hot (with the peak reached around 20-30 minutes on average), which would theoretically give more credence to the idea that they need warm up compared to a pair of headphones. That said, your example doesn't even apply, because you said that after they were warmed up for 15 hours, their sound permanently changed (which would mean that they sounded differently even after operating cold from there on in). In reality, they would need to reach the same temperature that they were at after your "burn in" for you to get that same sound signature. The only exception would be if the high temperatures damaged something in the tube during operation, which would permanently alter the sound signature -- but that would be indicative of a poorly-made tube and not representative of tubes as a whole.
I'm not hoping to sway you one way or another, as I can tell that's probably a fruitless endeavor. I'm just trying to stop you from spreading this pseudoscientific, harmful nonsense for other people to believe. Burn-in isn't real, it doesn't make any physical sense, and spreading the idea that it exists does nothing but cloud real, useful discussion about audio.