It is very simple physics problem. All you need is specific heat capacity of metal, weight and time any you should be able to work it out. Although some cooling losses  are neglected is this way.  

This can be obtained simply from  the first term of the solution of the heat out of a slab problem. The time dependence of temperature profiles may be represented by the relaxation time constants in the Fourier Sine series expansion, which are given by  thoj = h2 /(2j+1)2 Pi 2 D where   h  is the thickness,  D is the bulk heat conductivity.  This can take the following format in using the first term  j= 0 in the expansion, which is proven to be very good approximation:

For the long cylinder  Tho= d2 /4.8 2 D ;  Spherical peace  Tho = d2 /4 Pi2 D,    d  is the diameter,.     If  one  takes the   annealing  time= 3 tho, T= 95% To of the desired temperature will reached. If you take time = 4,  then  tho  T =98.2% To. 

T= To (1- exp -t/Tho )

GOOD LUCK

Murat: Unfortunately I am not able to attach a thermocouple to the metal I am baking.

David: The basic physics problem is what I've been looking to solve.  I usually work with 304 S/S, but this time I'm working with a cast aluminum.

Tarik: I like this example but how would this account for irregular shapes?  This is why I would rather go off of a total mass  equation if possible..  Currently I'm working on a giant aluminum star that is almost two feet in diameter & 1.5" thick.

Dear Kid, if one is an Engineer by birth, which ı am not,  then one  should know that we are always talking about the safety factors or clearance  etc.  in our calculations. Secondly,  knowing the mass and the  heat capacity  of one's  object , one  may  easily estimate  the  minimum amount of energy  necessary to  reach for a given temperature in our  furnace assuming that it is well insulated.  Then,  while we are selecting capacity of a furnace to take our  load or mass from the room temperature up to the desired temperature for a given time interval one has to know its minimum electric power handling capacity. But that is not enough'  We shouldn't forget in the heat transfer problems the surface area, and its properties (thr heat transfer coefficient)  play dominant role unless you are employing inductive heating.  Summary!  one has to be very well trained mechanical engineer with a good instinct to distinguish the trees from the forest or the main elements  of the design objective  from the secondary features!

 If you have irregular shapes either you may file them off  or  simply by taking the sharp edges and corners in your  simulations  using the properly selected boundary elements in the numerical computations.  Best Regards

Tarik: I think were getting off target here by getting into oven design....  If I were using an improper oven I would not be able to reach my target temperature < two minutes after putting 25-30 lbs of mass into it.  We're talking about an industrial batch oven for clarification & 400 degrees F. Internal area 4' x 4' x 3'.

Lastly the irregular shapes you speak of are not the same as what I meant.  To clarify: The difference between a rod, a star, a cube, or a even a clover.  I never know what my next project can be, so I prefer to calculate off of mass to identify total weight, instead of spending a lot of time calculating all the features exactly.

The initial conditions are:

The oven is @ 400 degrees F.  

The part is @ room temperature.

The part is then placed in the oven, & then the oven cools down by 60 degrees.

Then it recovers back to 400, in < 2 minutes time.

What boundary conditions are you looking for?

Kid:  if it is so trivial,  first of all why did you put that question to be discussed at this platform? The logical sequence for the process  you have been described above is incomplete!:

''The part is @ room temperature.The part is then placed in the oven, & then the oven cools down by 60 degrees.''

Where is the time interval for the isothermal annealing stage?  

Secondly are you serious taking about  isothermal annealing  of any metal and alloy at  400 F = 204 C other than few eutectic systems such as Sn-Pb 60/40 (soldering), which melts at 183-190 o C.  

Tarik:  May we please stick to my question? What is trivial is why you are insulting me in a place that is intended for people to discuss ideas and learn from each other. Never did I state that I am annealing, nor am I.  I did not give certain details to my process, because they are not relevant to the equation.  Like the size of the vent to pull the heat away from the oven when you open the door.  Once the question has been answered properly, we will have all the details to handle every situation.  If you only care to lecture instead of help then please stick to teaching.  

This should be a simple question and answer forum....  Please don't infer into my question.  If you don't know something, ask!  Otherwise, don't assume! 

If I have to do a real world scenario to prove this theory out, I will.  But It's nice to get intelligent answers from the scientific community, and compare them to my actual results.  

Although like I said before, I can't put a T/C on my parts, so I would have to do a simulated test to make that happen.  Those results can be misleading sometimes, so I like to compare them with the math as well.

Dear Kid,   Sorry you have misunderstood me.  Teaching the heat and mass transport course to the graduate ME students for a halve century,  I was somehow  astonished by  your empirical approach to the problem. Please read the following question you have made.

''If I put the metal in the oven and it takes 120 seconds for the oven to recover and reach target temperature, but I put 40 lbs of aluminum inside, is the metal also at target temperature?''

First of all you haven't specify the weight of the metal you put into oven that took 120 second to reach the target temperature then asking what happens if you put  40 lbs aluminum !!   Sorry I couldn't  got that question properly!

Tarik: This is great!  Now we're getting to an actual discussion.  With you teaching for so long you should be well versed in if the details are missing, questions and fact finding is necessary :)

I found a typo in my question and fixed it:   If I put 40 lbs of aluminum in my oven and it takes 120 seconds for the oven to recover and reach target temperature, is the metal also at target temperature?

Yet it still answers your question about weight : 40lbs (AL)

The one factor we haven't discussed yet is what causes the oven to drop in temperature? Is it the new mass of metal itself?  Or simply heat loss from the doors being open?

Can the oven recover just as quick regardless if it has a large metal placed in it or not?

These are questions I would expect from someone who has been teaching heat and mass transport for halve a century.

Dear Kid construct the cooling curve.(useful)