I think I see where you're going with this... you're recalling the lab where you're measuring the temperature of a substance undergoing a phase change, and as you add heat energy to the system, the temperature stops rising momentarily at the transition zone (solid to liquid, or liquid to gas), until finally all the solid changes to liquid or all of the liquid boils off and then the measured temperature starts going up again. And you're thinking that since the global average temperature seems to have leveled a bit during the past few years, we might sorta be in that transition point, so the average temperature will continue to stay steady for a bit, and them 'bam'! all the ice will melt and we'll start to see average temperatures start rising again?
Assuming that's what you mean, I see a few difficulties with that line of reasoning...
First, while maybe land temperatures have leveled off recently, it looks like average ocean temperatures have still been rising... http://www.ncdc.noaa.gov/cag/t... . I think people spend too much time studying land surface temperatures, which are pretty fickle.... heat rises, which causes low pressure areas which draws in air from high pressure areas -- which is usually from where it's cold. That probably happens somewhat with oceans too, but not to as large of an extent. Plus, we measure the temperature of oceans near the surface, we haven't really been measuring the temperature of the air up wherever all of the heat rises to. So the ocean temperatures are probably a much better measure of the Earth's climate, and they still seem to be rising fairly steadily.
Second, the arctic ice is melting and re-freezing every year, so we go already go through several of those phase change cycles annually. Yes, we've been "losing" sea ice and glacier coverage each year, but I don't think the heat energy absorbed by melting the ice is anywhere near as substantial as the extra heat energy absorbed from the sun once reflective ice melts away to expose dark landmass or open ocean. This accelerates the melting of any adjacent ice, and the fact that seasonal ice cover is melting earlier and earlier each spring should be cause for concern. But no one really lives up there anyway, so no one really cares if the arctic is missing its cold. But they do like to act surprised and smug when the arctic cold gets sucked way down south so they can complain that climate change can't be happening because it got colder instead of warmer. OTOH, much of the antarctic has been getting a slightly colder over the decades, my theory is because there isn't as much land area in the southern hemisphere to successfully pull the cold away.
http://svs.gsfc.nasa.gov/cgi-b...
Anyway, the Earth is pretty complex to boil down to a simple experiment you might do in a styrofoam cup. Ultimately, I believe the biosphere will do its best to adjust to the conditions to keep the temperature / humidity / air quality within an envelope suitable for life for most of the planet regardless of how much humans interfere or even how much or little energy it gets from the sun. That's how buffer systems work.
Speaking of buffer systems, that's probably a chemistry lab that's much more applicable (and scary). If you remember doing titration in chemistry, you might recall that adding drops of acid or base to pure water would have an immediate and linearly proportional impact to the pH of the water. However, add some buffer systems to that water (calcium carbonate or whatever), and the system response becomes nonlinear... You can add a bunch of hydrochloric acid to the solution and the pH will hold fairly steady, until the buffer is saturated and then BAM, the next drop of acid suddenly tips the pH of your system down almost to where you would have been if there was no buffer system in the first place. I kinda expect a similar thing to happen with respect to global sea levels, or to global temperatures, or more substantially to ocean acidification. It seems like we're so worried about carbon dioxide, which is an indicator for global warming, which is an indicator for global sea level rise, that we're probably going to fail to notice the collapse of the food supply due to ocean acidification and drought, which will likely be the main thing that ends up killing off the humans. But no one is riled enough to riot enough to change anything until food become scarce, so chances are we'll get the opportunity to see this all unfold (maybe not in your lifetime, but probably in my children's lifetime.
