Should I seal my hot leftovers before putting them in the fridge? I understand that I should put my hot leftovers straight into the fridge, to best avoid spoilage. And that if there are lots of leftovers, I should divide them into smaller containers to help them cool faster.
My question is: Should I put lids on those containers?
My two concerns are:

Will a lid, that traps hot air around the food, slow the cooling down too much?
Does sealing hot food &quot;sour&quot; it somehow?

For reference, I store my leftovers in these 16 oz. deli containers
Part of the challenge here might be your definition of &quot;hot.&quot;  When I think of &quot;left overs&quot;, I see what is left over after eating a meal.  It is certainly not &quot;piping hot&quot;, as in just off the stove.  There is no problem packaging, covering, and refrigerating these items.  As an alternate example, when I make a batch of chicken stock, once it is cool enough in the pot to deal with so I don't burn myself, I portion it into deli containers for freezing.  I cover (but sometimes don't completely seal, depending on how hot), and leave on the counter for 30 minutes to an hour before moving to the freezer.  These are just examples.
It seems to me that (as at least one link in another answer here states) waiting until your food is room temperature might be problematic, as this could easily place it in the danger zone for some time.
Putting a lid on a deli container is only a problem if the items inside are so hot that the lid bulges.  The issues is not food safety, but that the lid might be compromised or unseal.
Sealing does not cause spoilage.  Spoilage bacteria do that under proper conditions of temperature and time.
Bottom line:  Place your leftovers in a container, seal them, and refrigerate as soon as you are able to handle them, and within food safety parameters.