「掛けられたら」 here is passive voice, namely the famous "suffering passive". A person does something to you and you are not happy about it. You would not 怒鳴りつけちまう ("yell out loud") if you were not suffering, would you?
The three usages of 「れる・られる」 is explained here. Only the context will tell which one of the three meanings 「れる・られる」 is being used for. Please remember that Japanese is an incredibly contextual language. Had you asked just "What does 掛けられたら mean?", no one could have answered. Without any context, it could mean honorific, potential or passive voice.
"I would yell out loud if someone put a jacket on me on such a hot day like this."
I did no use the passive voice structure in my translation. You could replace the "if someone put a jacket on me" part by "if I were made to wear a jacket".