Do you need to cook tomato puree? I'm making a tomato sauce cold from tinned tomatoes and I was going to add tomato puree to thicken the sauce. Is it ok to use tomato puree without cooking it?
While it is perfectly safe to eat tomato puree without cooking it, it is not generally recommended.
Uncooked tomato puree in a sauce can be undesirably sour and have a rather raw, rough flavour.

If you don't mind this then go ahead, but I would recommend simmering the sauce for at least another 10 minutes after adding the puree.