What Is The Best Climate To Keep Coins In?

As far as temperature is concerned, the best climate is neither hot nor cold, but "constant". If a coin is exposed to constantly changing temperature, there is a risk that condensation will form on the coin, making it more vulnerable to oxidation and corrosion. Especially try to avoid storing coins in a cool place then bringing them out into a warm, humid environment.

Which leads to the next point: humidity, which is a far more important factor for coin storage and handling than temperature. If you can bring the humidity down to zero, it doesn't really matter what temperature they're at.

Not really an easy question. Normally the lower the temperature, the lower the humidity so at really lower temperatures, humidity drops to much safer levels for coins. Also, with lower humidity, you also loose the contaminates in the air that mix with that humidity. For example in many areas where Sulfur Rich Coal is burned, the air is contaminated with SO or SO2. This mixes with the H OH, otherwise known as water or humidity and becomes an acid. In some areas known as Acid rain and ruins anything Copper easily. So as you lower the tmeperature, you eliminate or mostly eliminate that problem.
On another note as you lower the temperature the metal in the coin shrinks and the coin becomes smaller and eventually may just vanish. Or if in an Album, fall out due to the coin now being to small for that slot.
As you raise the temperature of the invironment where the coins are stored, this heat could act as a toning, tanishing, corroding problem. Again, usually in hot areas though, humidity is also not to much of a factor. Note the Egyptian area ability to store even human remains, Mummies, for thousands of years due to very little humidity.
Note the very little rust on cars in the Arizona area due to high heat and little humidity.
To sum up your questions answers, there is no hope for long term storage of your coins unless you move to Egypt and place them in a Pyramid. Or move to Arizona and place all your coins in a car.
On a serious note though as long as you don't expose your coins to humid air or air that contains dangerous gasses, they should last a long, long time.