Pretty much, what Ianthas said is all correct.
In summary,
い-adjectives in their natural form modify nouns.
い-adjectives become adverbs by changing い to く.
The conjunction or て form of an い-adjective is formed by changing い into くて, not by simply appending て.
In addition, I think it's important to note that 木造 is in essence a noun that means 'made of wood'. It can be used strictly as a noun with that meaning (あの建物は木造です), or it can have の appended to it to make an adjective (あれは木造の建物です).
You cannot simply smash a noun into a noun and force the first noun to act as an adjective as you propose with 木造お寺.
If, for a particular descriptive noun, that kind of construction is allowed than dictionaries will note it as prefix rather than as a no-adjective. If that kind of construction is only allowed in specific cases, then those cases will have their own entries as compound words.
Most descriptive nouns, however, are specifically noted as na-adjectives, no-adjectives, or rarely as taru-adjectives -- sometimes as several of those forms. Some terms are arguably 'only' adjectives, and are noted in dictionaries strictly as a type of adjective and not allowed to exist as standalone nouns. Kind of an arbitrary distinction in pure grammar terms since anything before な、の or たる is arguably a noun, but distinguishing in the dictionary nouns that can also be adjectives and terms that can only appear as an adjective helps understand actual natural usage.
I think I may have rambled a little bit long on that, but I hope it helps. If I made any errors of fact, I welcome corrections from advanced learners and native speakers.