When you take your trimix course, you will learn that there is a "sweet spot" for different mixes as far as decompression obligations go. The variables, besides the mix, include the depth and the time.
Forgetting the oxygen toxicity issue for the moment, if you are going on a short dive to significant depth (other than the narcotic issue with regard to nitrogen), using helium for such a dive would actually increase your decompression obligation. This is because Helium diffuses much faster (about 2.65 times faster) than nitrogen into your tissues while, at the same time, your tissues can hold about three to five times more nitrogen than helium in them before becoming saturated. So, the helium rushes in and reaches saturation quickly compared to nitrogen on these kinds of dives. One gas is not the same as the others when it comes to the maximum amount the tissues can take before reaching saturation nor how fast the gas goes into the tissues.
When you start to increase time, eventually, either gas will reach saturation. Since your tissues hold less helium before reaching saturation, and because the helium will diffuse out more quickly than nitrogen, your decompression time will start to be less with helium mixes. It is a balancing act between depth and time.
A good depth to work this out with is about 150 feet. This is a depth where the old deep air divers have dived (I would never do this anymore; I am just talking academics here) without being totally blitzed with narcosis. For short durations, you will actually get out of the water sooner on air or with low amounts of helium in the mix (just enough to ward off narcosis). Start to stay longer, and you will get out of the water faster by increasing the helium in the mix. Deco time for air versus trimix at this depth converges at about one to two hours. Longer than this and helium becomes more efficient. On shorter and shallower dives, decompression is shortest on air, followed by trimix, followed by heliox.
One last however. Add back in the narcotic effect of nitrogen, and it becomes clear that it is better to do a longer decompression schedule without narcosis. Add to this the issue of oxygen toxicity on the deeper stuff, and you start to see that helium takes care of both of these issues at the small cost of a little time and thicker thermal underwear. It's worth it!
Helium is about six times more thermally conductive than air. It used to be thought that breathing it would actually hasten chilling. However, respiratory heat loss is actually LESS with Helium than with air. Because Helium is much less dense than air, it does not have the ability to draw out the body heat during respiration that was once believed. On the other hand, it makes a dandy air conditioner if you put it into your dry suit. So, argon in the suit (or even just air) takes care of the chilling problem while breathing helium mixes really doesn't do much in the way of chilling the diver.