They are both distinct wars, fought by different countries, in different era's. WW1 was the advent of modern military might, with a huge benefit for defensive positions, the battle theaters were (much more than in WW2) near the European continent, including Russia and middle east. That said, there are some arguments that can be made for WW2 being a continuation of the Great War.

The cooling off period you refer to is not so much that, as it is a period in which a lot of loose ends are not tied off. Remember that the Russians had had a revolution near the end of the war, tried to continue (as they had promised their allies), got overthrown again and were set back massively in terms of land, people and resources at the treaty of Brest-Litovsk. The harsh treatment caused temperaments to rise.

Temperaments rising is a major theme in the inter-war period. The same goes for the Middle-east where Arab support had been raised against the Ottomans, in turn for promises of Arab self-rule in the Kingdom of Hejaz. These ideas that later became known as the Hussein-McMahon correspondence, was overturned as the allies desperately needed Jewish support in the industrial push.

Apart from these parties there were of course the German people themselve. They had the idea that the war was lost because of weak generals capitulating (the famous stab-in-the-back myth).

So, sentiments are a big issue after the end of WW1, the idea that ends were not tied up. For the Germans, and to a lesser degree the Austrians as well, there had been forced upon them a peace settlement that they found to be much too harsh. To a certain extent the harshness expected, as repair payments had been heavy after the German-Franco war of 1870-71, and not to forget the blow to French honour at being crushed militarily and having lost the mine area of Alsace-Lorraine. The French were actually the biggest proponents of harsh peace terms, while the Americans sought a more concerting treatment of the defeated parties.

Also, as the name implies these days, 'World War', it was a war fought by a lot of belligerents. After the Great War the blame was put on the Germans, and especially the Prussians. Some even went so far as to say that the Prussians had walked a special way (the Sonderweg), that had led them to be such warmongers. To prevent any such hostilities from ever happening again, the French (mainly) tried to break up German might so they could never pose any danger again whatsoever.

In many ways Second World War, as historians often write, is a way for the defeated from the the Great War to get back a the winners. There are a lot more angles to it, especially also why it should not be seen as a continuation; I hope to get into that another time.

Most of my info comes from Jay Winter and Antoine Prost, The Great War in History. Debates and Controversies, 1914 to the Present (transl. Cambridge 2005); but also from a piece I wrote some time ago on Middle-east relations, but I seem to have misplaced the materials.

The usual arguments I've seen for treating WWI and WWII as a single conflict generally come from trying to look at it in the long term. Hundreds or thousands of years from now, how will they be seen?

And in that respect, they'll probably be viewed as a single turning point of warfare as we entered the modern era. Armies at the beginning of WWI were not terribly far off from the armies of the 19th century, and armies at the end of WWII were not terribly far off from the armies we have today. A lot of technologies were invented and came to maturity in that time span.

Plus, you also have the fact that many of the participants in Europe were the same (Germany fighting a two front war against Russia and France/UK/USA), with only a couple major powers switching sides. Many of the fundamental grudges, power struggles, and political forces were the same for both of the two wars. Part of the whole reason WWII happened was that there was not a decisive blow struck in WWI- everyone just stopped fighting. The fundamental tensions that caused the war didn't go away, and arguably got worse due to the myriad internal political problems that arose in the inter-war years, from Nazism to the Russian Revolution to the political climates in France and Britain.

Coupled with that you have prescient statements at the end of WWI like this one from Foch, on the signing of the Treaty of Versailles: "This is not a peace. It is an armistice for twenty years"

Nothing was really settled at the end of WWI. That was a big reason for some of the Allies' behavior in WWII- particularly the insistence on unconditional surrender and the initial postwar focus on removing the ability of Germany and Japan to make war.

They were certainly two separate conflicts, separated by decades of peace. But if you look at the broader historical forces both wars were symptoms of the same disease.