Hot water urn for dishes

On Shabbat, can I pour water from a hot water urn into a mug and then pour from that mug onto dirty dishes to help clean them? I find it very hard to do dishes with just cold water.

Great idea.

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Doesn’t the hot water from the urn that one pours onto the dishes have to already be in a kli shlishi Before one pours it onto the dishes? Otherwise it might be cooking? Pouring from the urn into the first clean dry cup would put the water at the status of only “outpourings of a kli rishon”? So, two more clean dry cups to our that water into, in succession, before pouring it on the dishes. Would the outpourings of a kli sheini poured onto the dishes be sufficient? I’m not this well versed.
Toda rabba. Yakov Moshe

Nothing is being cooked in the first cup. It can be used to pour onto other items without worry of cooking