MikeFerrara:Breathing helium doesn't make you colder, although, using it in your dry suit will.
One reason not to use heliox is that most of us can't get a tank full without a booster. I mix trimix by transfilling helium, some O2 and then topping with air. With a continuous flow system you can use it to make trimix directly or transfill helium and then top with nitrox. Either way there's no getting around having some nitrogen in there.
When I say we can't get a tank full without the air/nitrox top from a compressor it's because the hightest pressure tanks we can get from the gas supplier are 2600 psi and sometimes we have trouble getting them much over 2000 psi. So...to partial pressure blend heliox and get your tank full you'll need a booster.
But, some divers and shops have boosters and these days more than a few divers are using heliox for decompression such as 50% O2 and 50% helium for a 70 ft gas switch in place of EAN50.
At very deep depths some nitrogen helps minimize HPNS also but most of us don't go deep enough to worry about that.
After doing a quick search on the subject, it turns out that Helium is apparently conducting less heat away from your body through respiration than air, due to its low heat capacity (Nuckols et al 1996, Schmidt 1982). (Presumably it conducts heat better than air, but carries it less poorly, so that the transport of the gas from the lungs through to the regulator, allows the gas to cool to the surrounding temperature much faster than air, and hence the air you breathe out is cooler than air would be, leaving more heat within your body... ?! Not sure I entirely understand this myself.. But hey...)
Edit: Just realized this one had been answered in far more detail by DSD and padiScubaPro - So refer to the detailed explanations on the previous page for explanations.
I too was under the impression that helium rich breathing gasses would accelerate heatloss, but it seems I was mistaken, and that is only the case when you use them as a drysuit inflator gas.
On that subject, I've been told Argon when combined with perspiration, will actually form a rather acidic liquid, and that commercial divers (Using argon as drysuit inflator gasses extensively) found that the drysuits had a substantially shorter lifespan when using argon than when air was used.
Not sure about the accuracy of this one - But so I was told anyway.