I would prefer to keep it at room temp., not chilled, and the box doesn't say to 'refrigerate after opening', but just to be sure...
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you haven't said why you want it at room temp or when you plan to use it or for what recipe! if you plan to use it w/in 24 hours of opening it, it might be o.k. at room tempo, but i think it begins fermenting pretty quickly if not chilled. if you can, i'd advise chilling it and then removing it from the frig 2 hours before using it, if you have to work with it at room temp. And I am normally not very rule-following, btw.
I wanted to try it in a peanut butter sandwich (I've heard good things), and if it turned out well I could keep leftover puree on the counter for when cravings hit. I suppose the possibility of spoilage isn't worth the benefit of avoiding a chilly sandwich, so I'll refrigerate. Thank you!
it's not going to have a long life in your frig after it is opened so keep in the freezer(easy to scoop or dig out after softening a few minutes). If you like the flavor combo of peanut butter and pumpkin, consider that that combo can be found in a number of African dishes. Consider making a batch of soup w/: ~ sauteed onion and garlic, pumpkin and some pnut butter and a little tomato paste and chicken stock, or google for recipes.