I am not sure about the difference between using "ly-formed adverbs" and using "sole adjectives" before "present participle adjectives".
I think in the first sentence "relentless" qualify "beating heat" , in the second sentence "relentlessly" qualify the "beating" ?
1-The relentless beating heat was beginning to confuse me. (sole adjective)
2-The relentlessly beating heat was beginning to confuse me. (ly-formed adverb)