@Disinterred
Oops, didn't read the question though. If graduate though, I recommend Jackson.
In my second year undergrad we used Griffiths. Thats a nice book.
Although in hindsight, probably won't help now
Null, might that be Chabay and Sherwood?
A very comprehensive text that also has loads of problems Jackson, Classical Electrodynamics. It is a graduate level text though...
This is a classic 'Carnot refridgerator' problem...
EDIT: Maybe this will help.
http://www.ohio.edu/people/piccard/phys202/carnot/carnot.html
Find an expression for the heat leakage first(through the walls).
I believe you should use a energy argument.
1. Construct a differential eq. from cons. of energy expression. (Drawing a diagram helps)
2. Solve.(Should be SH considering small displacements)
3. ect.
The most difficult part is getting the PE and KE right...this is what the diagram is...
The mass of the sun is a known quantity which you can lookup. You could derive vis viva from what the question gives you though...
edit:I don't think you even need the period TBH