Originally Posted by Doug Blackburn
The bottom line is that you can never know which setting is closest to 6500K without a meter. You can't accurately tell your body temperature without a thermometer. Either way, you MAY be able to tell if you are way off, one way or the other, but you can't tell if you're on the money or not. Your eyes adapt over time to whatever you watch on TV... if you've been watching 7500K images for days or weeks or longer, 6500K is going to initially look wrong to you and it can take hours or days of getting used to what 6500K looks like before it begins to look normal and 7500K looks too blue.
The owner's forum for the model of display you own, or published product reviews of your model, are possibly the best sources for finding out which of the color temp settings are closest to 6500k. In many cases, you'll have one choice that's warmer than 6500K and a second choice that's cooler than 6500K with neither setting being "right". Which is one of the reasons people learn (and spend money on calibration gear) calibration or pay for professional calibration. That's the only way to know that your color temp (and other factors) are as accurate as your TV can be.
Agree with pretty much everything Doug says here.
If you don't have a meter, and just want to know which mode on the display is closest to 6500K or D65, another option is an optical comparator. All you need for that is a reasonably accurate 6500K bulb and a spectrally neutral white card. (For front projection, the screen will serve for the latter.) There are quite a few potential stumbling blocks to this approach though, and mitigating them could be more hassle than obtaining a relatively low-cost color meter.
Spectrally neutral white cards don't grow on trees for example. Even most photo gray and white cards (including Kodak's) don't fit the bill, because they're typically designed for exposure/f-stop adjustment, rather than white balance. The X-Rite white cards are probably the most accurate, but they cost almost as much as a cheap colorimeter.
If you're on a tight budget, one way to find a relatively neutral white card is simply to take some paper/card stock samples to a photo supply shop and borrow their X-Rite cards for comparison. (The comparison needs to be done in natural daylight btw. Artificial lighting will not work.) Most off-the-shelf paper and card stocks will be either too blue or too yellow. Neutral papers will appear sort of ivory-colored. "Clay-coated" card/cardboard stocks may be a good bet. The photo shop may have some specialty photo papers that are relatively neutral as well (most off-the-shelf photo papers also tend to be on the blue-er side).