You should be able to do that with MCNP4.
You need to find the documents directory in your install. It should include a user manual. Also there should be a theory manual. If you've got source code there should be a developer's manual. IIRC, back in MCNP4 days they routinely included the source code so you might have it. Read up on how to set up the cells with the materials. Read up about tallies of type F6 (heat deposition) and F7 (fission energy) particularly. Then you will need to know the number of neutrons per second the source releases and use that to normalize everything. The tallies report their results in "per particle started." So you convert to "per second" by using the neutrons per second the source releases.
Also, carefully read about the SDEF card. This is the source definition card. It allows you to specify the location and energy of source particles.
Other possible things you might be interested in are F4 tallies. These give you the particle flux. You could also investigate things like the total number of neutrons generated from any given source neutron. This gives you an estimate of how close to criticality your reactor is. (Hmm... The spell checker on Physics Forums does not know criticality. Hmm...) You could compare that to what you get from a KCODE calculation, which you should also read up on.
You may want to play around with your geometry. For example, just because the material in a sphere is all the same you don't automatically want just a single sphere. You might want some spherical shells to allow you to refine your tallies. Maybe you want to figure out how much heat gets deposited in each layer.
Probably as a first pass through you want to use neutrons only. Once you get your geometry and materials correct, and you are happy with your SDEF and tallies, then you might want to add photons. This means you will need to read up on the MODE card, and possibly about the PHYS card. Some things you will be limited by the available cross section libraries.