How much of a GPU's electrical usage is probably turned into a increase in air temperature?
My numbers might not be exactly accurate, but I would say that about
99.99% of the energy that enters the GPU, and even CPU is converted into heat.
The other .01%, is the actual signal out of the GPU to your display.
The job of the GPU is to take in a lot of data, and process it, requiring a lot of calculations. These calculations consume energy, producing heat, and eventually a result.
Now it is important to note that while this says that it is a 375W card, it will not be drawing 375W the entire time it is in operation. Just like your CPU, your GPU will only do as much as you need it to, and may step down <100W.
Simply browsing around your windows desktop, the card it doing next to nothing, and will draw next to nothing; but launch Crysis, and your frequency mill max out and the card will start drawing its maximum rating.
Basically it all goes to heat. Inside the chip there are billions of tiny transistors, each one acts like a really tiny switch. These transistors are connected to form various logic functions. Due to the geometry of the transistors, they all have small parisitic capacitances. Whenever the logic changes state, which is on average the same rate as the clock, these capacitances need to be charged and discharged. The current to do this has to pass through the transistors, which have some resistance. Resistance and current flow mean voltage drop, and volts times amps is power. Every time the clock cycles, power is consumed charging and discharging these capacitors. This happens in every integrated circuit - your GPU, your CPU, your RAM, your hard drive controller, your cell phone, etc. This is why when you overclock your CPU or GPU, it uses more power and generates more heat. This is also why your laptop will vary its clock speed on the fly to save power instead of just letting the CPU run idle.
In terms of how much doesn't go to heat, it isn't very much. A watt or two for the fan. Maybe. Perhaps hundred milliwatts for the LEDs, if the card has a bunch. A couple of milliwats get moved over the PCI express bus, to get absorbed in terminations on the other end of the bus. A couple more milliwats get sent out over the DVI or HDMI port to get absorbed in terminations on the other end. All in all, with a TDP off 375 watts, less than 0.1 percent of the power coming from the PSU doesn't get directly dissipated as heat.