Let's say I am a pretty skinny guy with a fat thigh. Is it possible to lose fat exclusively in some part of the body? For example, is it possible to lose thigh fat while not losing any weight in my upper body?
Nope, it's completely impossible to target and reduce fat in one spot on your body. The only way to lose fat in your thighs is to lose fat everywhere.
On the other hand, you can target and improve the look of a specific body part. For your thighs I would suggest squats (but I suggest those for just about anything). Simply sprinting would help the shapeliness of your legs overall.
You cannot target specific areas of your body to lose fat*. See this answer to a similar question.
It's called the Spot Reduction Myth. I explained it in this answer:
Belief in spot reduction means that you think exercising your arms/abs/thighs/butt will specifically reduce the amount of fat on that area of your body. This is a misunderstanding. As exrx.net describes:
Contrary to what the infomercials suggest there is no such thing as spot reduction. Fat is lost throughout the body in a pattern dependent upon genetics, sex (hormones), and age. Overall body fat must be reduced to lose fat in any particular area. Although fat is lost or gained throughout the body it seems the first area to get fat, or the last area to become lean, is the midsection (in men and some women, especially after menopause) and hips and thighs (in women and few men). Sit-ups, crunches, leg-hip raises, leg raises, hip adduction, hip abduction, etc. will only exercise the muscles under the fat.
In other words, you can't "tone" your little bulge. You need to exercise your whole body and eat less or eat better.
Your body determines where it will remove fat. You can, however, tell your body where to build muscle, which is totally more awesome anyway.
(* Technically, there is some research popularized by Tim Ferriss that suggests that there might be a way to target fat reduction through the mechanism of more blood flow, but the science is nascent. Even if true, it still wouldn't be the most productive way to lose fat. I beg you to ignore it.)
As Sparafusile said, you can't target fat loss effectively. Try adding mass to your upper body instead to look more proportional.
Also, with regards to Sparafusile's suggestion of doing leg exercises, this will certainly help with improving their composition. They might not lose size, but instead of looking flabby, they'll start to look more toned.
You cannot target specific body parts for fat reduction - you can target certain areas for muscle growth - but this is usually not recommended. Depending on your genetic make up, gender and age you will have different locations on your body where fat cells are more prevalent. You will need to reduce overall body fat (bf%) in order to see a reduction in those areas you're interested in.