Verbs that end "ing" describe things that are happening presently or is ongoing. This is known as present participle. "To help" "to distribute" is not necessary. "To help distribute" implies the same meaning, and the sentence is simple. I know that might sound confusing, but the main point is not to use "distributing" when reading about an action that took place in the fast or will take place in the future. All "ing" verbs will describe something that is taking place at the current moment or is a part of an ongoing process. Hope that was helpful. Let me know if you have any questions.

Also, to use "distributing," you would say " to help with distributing the heat."

The difference is one of form only. There is no difference in meaning. to-infinitive or bare infinitive Help is a verb that can be used with or without to and with or without an object before the infinitive. When we use it without an infinitive it sometimes sounds more informal. Compare the following: Could you help me to look for my car keys? I can't find them anywhere. Could you help me look for my car keys? I can't find them anywhere. Would you like to help to cook dinner tonight? It's late and I'm feeling tired. Would you like to help cook dinner tonight? It's late and I'm feeling tired.