"They spike up very quickly after the ice age ends, drop back down, and generally fluctuate a significant amount without any human input at all.
Not according to any the historical temperature graphs [wikipedia.org] that I've seen. The temperature rises rapidly at the end of the ice age and then levels off an eventually begins to fall again.
The graph in the page you linked to shows temperature doing exactly what I claimed it does."
Acually it does not. The spikes you talk about are changes of about 0.3 degrees Celsius during hundred of years. Check the diagram more closely and you will also see that. The last "downspike" is what's called the little ice age and is still just about a dip which is about half a degree during a couple of hundred of years.
Never before in history has the temperature changed with more then 1 degree over 100 years. Even the during the sharp raise in the beginning in the diagram was that the case.
Natural variation in temperature are very slow and does not change as fast as today. The variations in temperature we see today are unprecedented for the last 10 000 years. Thats why scientist are saying its AGW. We, humankind has caused it.