Serve Hashem with Warmth
One of the primary segulos of Chanukah lecht is that with it, we merit children talmidei chachamim.
Someone once became a Rav, a leader of a community, and he asked the Rayatz of Lubavitz zt'l for counsel. How should he give mussar and direct his kehillah in the path of the Torah?
The Rayatz replied with a mashal: A wealthy person went to a hot bath resort. As he bathed in the hot springs, someone gave him a massage. The rich man enjoyed the massage immensely. Every time the massager beat the wealthy person and forcibly bent his muscles, the wealthy man emitted sounds of "Ahhh!" showing that he enjoyed it. After the massage, he paid the person who hit him.
There was a poor person there. He thought that the wealthy person enjoyed being hit. So he followed the wealthy man home, and when they were outside the rich man's home, the poor man hit him several times. "Isn't this great?" the poor man said with a smile. "You probably enjoy it immensely!" The wealthy man shouted at him angrily. The poor man didn't catch on yet and asked the rich man to pay him for his exemplary service. The wealthy man called the police and had him removed from his grounds. The poor man didn't understand what he did wrong and why he wasn't paid like the person at the hot bath resort. One day, he gathered courage and returned to the wealthy person with humility and tears and asked for an explanation. The rich man understood that he sincerely wanted to understand, so he explained it to him. "When I am in a sauna, each hit that I receive goes deeply into my flesh, and it is good for me emotionally and physically. I am willing to pay a lot of money for a massage. But you hit me without any heat... and therefore, you deserved to be punished."
The Rayatz explained to the new Rav that if he wanted to give mussar to people, there had to be a lot of love and warmth, and then they would accept his teachings. But if he told them how to act without giving them any kind words, warmth, and love, they wouldn't want to listen to what he tells them.
We can say that this is hinted in the Chazal, חכמים תלמידי בנים לו הויין בנר הרגיל, "When one is accustomed to lighting Chanukah lecht, he will merit children talmidei chachamim." Fire is hot. This hints that with warmth and love, you can merit raising your children to Torah and to yiras Shamayim.
The Gemara also says there, בציצית הזהיר יין גרבי וממלא זוכה היום בקידוש הזהיר ,נאה לטלית זוכה, "When one is cautious with the mitzvah of tzitzis, he merits beautiful clothing. When one is cautious with kiddush on Shabbos, he merits having barrels of wine." These times the word הזהיר "When one is cautious" is used. Whereas, when it discusses lighting Chanukah lecht, the Gemara says בנר הרגיל, when he is accustomed to lighting Chanukah lecht. Shem Mishmuel (5680) explains that the Gemara is hinting to us בנר הרגיל, one should become accustomed to serving Hashem with "a fire," with hislahavus.
This can be hinted in the words (Tehillim 132:17) ִיִׁיחְשלִמ נֵר ִּיַכְתָרע, " I have set up a lamp for My anointed/Moshiach." When mitzvos are performed with warmth, it brings Moshiach.
It states (Malachim 1, 1:1) בימים בא זקן דוד והמלך לו יחם ולא בבגדים ויכסהו, "And the king Dovid was old, he came into his old age, and they covered him with clothes, but he was not warmed." Rebbe Hirsh Riminover zt'l (Be'eros Hamayim, Toldos, Haftarah) explained that Dovid represents Moshiach. בימים בא, it was time for Moshiach to come, but the people were performing mitzvos without warmth, and therefore he didn't come yet.