The problem with the right-of-way rules is that they not only rely on each aircraft being aware of the other but also that at least one of them is going to take appropriate avoiding action. Whomever has the right of way is essentially irrelevant if either pilot is unaware of the other traffic, and even if you think you have the right of way do you really want to rely on the other pilot to do the right thing?
There are in fact no regulations prohibiting straight-in approaches at non-towered airports because the FAA does not regulate pattern entry procedures. However, just like any other approach to an airport environment, pilots executing a straight-in approach should not disrupt the flow of other traffic arriving at and departing from the airport.
Increased performance due to colder than standard temperature is a good thing, but it can take inexperienced pilots by surprise when the airplane leaps off the runway in less than 400 feet and reaches traffic pattern altitude with alarming efficiency! Better performance changes a few things that might come as a surprise to students and newer pilots. In addition to a shockingly shorter takeoff roll, climb performance will also be greatly improved in colder temps. So how does all this affect aircraft in the traffic pattern? The first factor is that when your takeoff ground roll is shorter, your climb out begins sooner. Combined with a much steeper rate of climb, you will reach the point of turning crosswind (300 feet below traffic pattern altitude) in a shorter distance than usual. When you make your turn to downwind you might find yourself already pretty close to the midfield downwind position. Because you covered less distance in the upwind leg, there will be a shorter distance than you might normally expect in the downwind leg.