Question

Objects a, b, and c are at different temperatures, a lowest and c highest. the three objects are put in thermal contact with each other simultaneously. without doing a calculation, is it possible to determine whether object b will gain or lose thermal energy?

Answer 1

No it's not
Assume a has a temp of 0C and c of 50C
b can have any temperature within this range if it is closer to 0C then it will gain thermal energy from c more than losing to a.
Moreover this will depend on the mass and type of material (specific heat of the object)