It seems impossible to give a general rule but some patterns can clearly be made out:
A) If the abbreviation of the noun is marked by a point, only the first letter has a
Jh. -> Jahrhundert
Abb. -> Abbildung
Jgg. -> Jahrgänge
The reason for this seems to be that the point takes the function of marking the abbreviation, so that it is not necessary to use capitals inside the word to mark it.
In the sentence
Im vierten Jh. vor Christus
"Jh." is no valid word so that the point must serve as abbreviation; thus you don´t need to use "JH."
But f.ex. in some technical languages, this can be different.
Dies steht in BGBl. 17 vom 23.11.2010.
B) If no point is used, capitals inside the abbreviation can be used to mark it clearly.
It seems to depend on the position of the letter that is used in the abbreviation, in the abbreviated word:
1) Letters which mark the beginning of a discrete part of the noun, such as
a) a sub-noun/-adjective
AKW -> Atomkraftwerk
Usually, these letters are capitals, but sometimes they are not:
letters not at the beginning of the word in some abbreviations
Pkw -> Personenkraftwagen
Hbf -> Hauptbahnhof
letters used to abbreviate some units
km -> Kilometer
ml -> Milliliter
EL -> Esslöffel
The question why this is so, is very interesting and I must admit I have no sweeping idea yet.
The exceptions apply to very well known, frequently used nouns and the abbreviations are clearly marked as such. Perhaps an abbreviation such as "el" is not clear enough from the user's point of view.
b) a syllable
Here, the same is true.
VO -> Verordnung (Ver-ordnung)
If the letter used in the abbreviation is none of these, it is usually no capital:
Na -> Natrium
MHz -> Megahertz