The word hermology isn't in the dictionary. The word you're looking is most like homology.
Definition of homology (from Merriam-Webster.com):
plural homologies
1
: a similarity often attributable to common origin
2
a: likeness in structure between parts of different organisms (such as the wing of a bat and the human arm) due to evolutionary differentiation from a corresponding part in a common ancestor — compare analogyb : correspondence in structure between a series of parts (such as vertebrae) in the same individual
3
: similarity of nucleotide or amino acid sequence (as in nucleic acids or proteins)
4
: a branch of the theory of topology concerned with partitioning space into geometric components (such as points, lines, and triangles) and with the study of the number and interrelationships of these components especially by the use of group theory —called also homology theory — compare cohomology
Other possible terms include:
thermology - the science of heat.
herbology - the study or collecting of herbs, especially as a hobby.