From my extremely limited knowledge, I also recall people saying that the world goes through different cycles of warming and cooling.
This sounds a little weird, the climate and the factors that determine it are well understood. I don't think you can separate the climate into exclusively short term/long term and "cooling/warming" phases. Generally a scientist would say "an increase in co2/solar input/milankovitch cycle, caused a drop/rise in temperature". Not "the earth was in a cooling phase for 300 years".
A video on the subject:
Prior to 1700 or so, we were in a cooling phase and we have since been in a warming phase. The argument here is that the world at time has been much hotter naturally and much colder naturally and that comparing the last 300 years to the previous is bogus for this reason.
The global temperature has been 'relatively' stable for the last few thousand years, but there have been a few drops/rises if you look at the records. Wiki is a good start:
http://en.wikipedia.org/wiki/Temperature_record
You might be referring to the "little ice age" as the "cooling phase". But quite simply, scientists have a good idea of what factors caused that to happen, and whether much of that is still relevant to today's climate.
http://en.wikipedia.org/wiki/Little_Ice_Age#Causes They outline orbital cycles, solar activity and volcanic activity as the main contributors to the changes in climate at the time.
People who think it's "bogas" to look at the last 200 years of our climate record because of something that happened in the past are just simplifying the issue too much (and are flat out wrong). Scientists are aware of the main drivers of climate and have a good idea of how they relate to both today, and 300 years ago.
Scientists do the maths and conclude increasing the greenhouse effect can change the climate significantly in a few hundred years. Just because "the climate changed before" doesn't disprove anything, it's a poorly thought out response to scientists.
From someone that spends a significant amount of time (albeit in finance) making predictions and forecasts, this sticks out to me as data mining or fitting the figures around an outcome that the scientists desire.
The only way you could come to that conclusion is with a lack of understanding of how scientists study/determine the climate. The video I posted above is pretty good covering the basics, even if you don't agree with his overall conclusion (which isn't an opinion, he's just explaining what scientists conclude).
Obviously this could only be the case if the world does go through warming and cooling cycles like I have heard. Does it and do those periods of warming and cooling fit roughly with those time frames?
This "warming/cooling" phase sounds like nonsense (it's not how scientists describe the climate in any sense). The global climate is historically determined by a few key factors. You could probably list all the different combinations of solar input, greenhouse effect and orbital cycles - split them into 3 different groups "warming, cooling and stable" phases and look at it that way. But I doubt that's what you are talking about here, rather just someone trying to over-simplify the issue an in attempt to discredit simple facts about today's climate.
Karl might come along and try to tie solar irradience to account for all the recent changes in the climate. But as far as I'm aware of there is no credible journals or universities supporting this conclusion (probably because there isn't enough evidence supporting it). But that wont stop him. I'm not even sure what it would prove, the Greenhouse Effect is still a key factor in determining the climate, and for as long as it's increasing, the amount of energy in the system will increase, which will eventually push up the temperature (and already has). Here is a graph plotting sun activity against co2 and temps:
http://en.wikipedia.org/wiki/File:Temp-sunspot-co2.svg
But don't take my word, or Karl's word for it. Contact your local experts on the matter (maybe a university or something), get them to explain the science to you (or ask where you could find information from experts). Unless you think the thousands of smart people studying the climate at universities around our country are all tieing themselves to work that's either a hoax, or not valid physics, in which case there isn't much anyone can do to help. All sorts of crackpots say that about financial/economic forecasters don't they? But it can all be put down to their ignorance at the end of the day. (ps, I doubt you are someone who thinks like that, but there have been a few people entering this thread who do seem think like that)