IMHO your unfinished compost would make an excellent tea. It will be as good as the materials you used in making it. No need to buy stuff. Don't worry about your pile going cold. My bins go cold after the first turning. One or two turns is all they get.
Bill Hill

All compost piles go cool, and more quickly than you might think, esp in the small home pile. With the correct amount of ingredients, moisture and air, the temperature goes up sharply, and then drops down more gradually. If you introduce more air into the pile by turning it again after it cools down, it will heat up again. When you turn it and it doesn't heat up again, it's 'finished'.

There is a graph in the link below that shows how transient that heat-up is.

Sue

Here is a link that might be useful: Compost heat graph

IMO, compost tea should only be made with mature/finished compost. Raw organic matter from a compost pile could contain dangerous pathogens that will breed and be spread in the tea. Better to be safe than sorry as has been said many times IMO...

Blutranes

We have conflicting opinions here. I would defer to blutraneÂs suggestion. His knowledge, skill and experience dwarf mine.
Bill Hill

I thought yours was a typo Bill, thus I only wanted to make sure the member had the right idea. I thank you for your kind words...

Blutranes