てならない: feelings and thoughts that arise involuntarily
Read persistent worries, feelings, and judgments. Distinguish the prohibition てはならない and take care about claims concerning another person's inner feelings.
Something stays in mind regardless of one's will
家族のことが心配でなりません。 means being extremely worried about one's family. It describes an involuntary feeling, not a prohibition against worrying.
あの時の言葉が気になってなりません。 means that words spoken at that time keep troubling the speaker. The connective 気になって from 気になる leads into the expression of a strongly recurring state.
Forms involving feelings and judgments
この方法には無理があるように思えてなりません。 means that the speaker cannot help feeling that this method is unworkable. It describes a persistent judgment, not a report of scientific proof.
The expression naturally conveys inner feelings directly. For someone else, 彼は心配でならないと言っていました can identify the evidence: he said that he was extremely worried.
は changes the expression into a prohibition
忘れてはなりません。 means that one must not forget. 思い出されてなりません。 says that something keeps coming to mind. Check both the presence of は after て and the preceding verb's meaning.
暑くてたまらない readily expresses an intense physical sensation. てならない fits worries or thoughts that arise involuntarily, but the expressions' uses should not be placed on a fixed intensity scale.
Quick check: Does 結果が気になってなりません。 say that one must not care about the result?
Show the answer and why
No. It says the result is intensely on the speaker's mind. Prohibition uses てはならない; that は is absent here.