That's a nice option if you have exposed bedrock next to your deck.
Here's an interesting description of using a high mass barrel vault oven:
It takes minimum three firings separated maximum 24 hours to heat the outer parts of the oven core enough to contribute to a stable temperature in the oven. Preferably four to five fires over a couple of days should be used to fully store heat in the thermal mass. After that only smaller daily fires are needed, for example in the morning, to have the oven ready for use in the afternoon and evening.
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