To begin, let's look at Christchurch, New Zealand 100 million years in the past. According to this map, the entire island of New Zealand is in the polar region. It is also much closer to larger land masses. This would have huge effects on the climate. The area would receive little to no precipitation and the annual temperatures would drop over 40 degrees Celsius. Also, the temperature variation of the seasons would increase from an average of 15 degrees Celsius to an average of 40 degrees Celsius. This would happen because the climate of the island would not be controlled by the ocean like it is today. This region would only be influenced by polar continental air masses. The ocean would still have an impact but there are no warm currents near the south pole. A climograph for this location at this time would look something like this...
A climograph of Christchurch so a much smaller diurnal temperature variation as well as much high rainfall levels given that is is now a maritime climate, instead of polar.
Now, take a look at where Christchurch would be 100 million years in the future. This map is based on continental drifts from the past and estimations of where it would lead in the future. This is also based on the assumption that Earth will still exist that far into the future. As you can see, this map predicts New Zealand will move so far north that is will be cut in half by the Equator. This would also shift the climate drastically. With much warmer water surrounding the island, rainfall levels would nearly quadruple. Moving closer to large land masses would also assist in the rise of rainfall. Being this close to the equator and receiving this much rainfall would contribute greatly to the reduction in variation of diurnal temperatures in the area. The humidity would skyrocket; not that it's low currently, but it would be significant. Given higher rainfalls and steady temperatures, a climograph of the regions future would look similar to the one below...
Christchurch, and New Zealand in general, has made and will make some very significant travels in its time. It managed to make is from the south pole, up to the mid-latitudes of the southern hemisphere, and will just make it to the northern hemisphere. It is a place that will experience several climates throughout its time; except continental. This island seperated from the pack and will not rejoin a continent for a minimum of 100 million years.