Basically a hair dryer has three major components; a switch, a fan and a heating element. The switch turns it on/off, modern hair dryers often have cold buttons as well as speed switches. The fan blows cool air from the back of the hair dryer to the front. The heating element warms the air as it passes through the front. It sounds like the heating element has gone out on your hair dryer since it's still turning on and blowing, it just isn't warming the air.
Someone put together an iFixit guide for replacing the heating element in a hair dryer but the model and process will likely be slightly different for you.
[guide|11257|Installing hair dyer heating element]
It does sound like it will involve soldering and to be honest I'm not sure where you could even acquire a replacement heating element. With that in mind this might, and I hate to say this, be a situation where replacement is the better option.
Before replacing though you might check some general electronic repair shops in your area, they may be able to repair it for less than the cost of a new one.
Hopefully it works out for you!