You could probably calculate a reasonable specific heat from the information here (thickness of the steel pipe is important, also). Just add up every component you know: (total mass of steel)*(specific heat of steel) + (total mass of dry soil)*(specific heat of dry soil) + (total mass of water)*(specific heat of water) = total specific heat. Of course, you would have to calculate the "mass of dry soil" by subtracting out the water. The water gives its own complications, as Simon mentioned. To do it right, you should take liquid water's specific heat for the first 50° (up to boiling), then steam's specific heat for the rest of the temperature change, and remember to include the heat of vaporization in at the end of the problem.
Total energy input required = (Total specific heat)*(Total temperature change) + (mass of water)*(latent heat of water vaporization)
You can just take the average value of specific heat of water/steam over this range, which is 2.3 J/g*°C. I just did a weighted average of liquid vs vaporous water. Then you can just plug this into the equation at the top, and plug that answer into the total energy equation.
The much harder part of the problem is figuring out the rate of heat (energy) transfer from the oven's air to the steel. You can use Newton's law of cooling (also applies to heating) to account for the changing temperature difference (rate of energy transfer is proportional to the difference in temperature). However, you still need an initial condition. Somehow, you have to get a number for a total rate of energy transfer to the steel, and I don't know the right way to approach this problem. Maybe you could try calculating the rate of air molecules hitting the pipe, and assume the air leaves at the temperature of the pipe? The specific heat of air is known, of course. A oven with a breeze inside would be dramatically different from a static oven, the latter requiring some convection dynamics to approach (how fast does fresh hot air replace the cooled air surrounding the pipe)?