Ok I'm not sure if some of the MCs are what you consider too cold since that's a bit vague but none of them should be stupid/naive in my opinion at least. Would you consider the MC of 'Death Is The Only Ending For The Villainess' and 'The Golden Haired Wizard' as too cold? Or do you mean extremes like in 'The Way to Protect the Female Lead's Older Brother'? Here are some recommendations that could be interesting for you (pls tell me which ones you don't like so I can give better recommendations in the future):
National School Prince Is A Girl
Princess Wars
I Was Just An Ordinary Lady
Valentine's Kiss Webtoon
The Evil Lady's Hero
The Villainess Lives Twice
The Villainess Reverses the Hourglass
Life in Another World as a Housekeeping Mage
Priscilla's Marriage Request
The Former Structural Researchers Story of Otherworldly Adventure
The Banished Villainess! Living the Leisurely Life of a Nun Making Revolutionary Church Food
The Stereotypical Life of a Reincarnated Lady
I Met the Male Lead in Prison Webtoon
The Youngest Princess
I'm Stanning the Prince
The Emperor Hopes for the Court Lady as His Bride
Aku no Joou no Kiseki
I Choose the Emperor Ending
The Princess' Spaceship
The Duchess with an Empty Soul
Lucia
Shindou Sefiria No Gekokujou Program
Holy Guardian Tiger
E? Heibon Desu Yo??
Daughter of the Emperor
Lady Baby
The Duchess' 50 Tea Recipes
Dad is a Hero, Mom is a Spirit, I'm a Reincarnator
Survive as the Hero's Wife
The White Cat That Swore Vengeance Was Just Lazing on the Dragon Kings Lap
Ascendance of a Bookworm
The Small Sage Will Try Her Best In the Different World from Lv. 1!
The Abandoned Empress (may be a bit cold)
The Justice of Villainous Woman
Chitra Webtoon
Of course, I'll claim Palimony!
The Crazy Adventures of Mystical Doctor
Koushaku Reijou no Tashinami
The Reason Why Raeliana Ended up at the Duke's Mansion
This Girl is a Little Wild
Doctor Elise
I’m a Villainous Daughter, so I’m going to keep the Last Boss
I Said Make My Abilities Average!
Isekai de Mofumofu Nadenade Suru Tame ni Ganbattemasu.
The Ghostly Doctor
Special Agent K
Otome Game no Hametsu Flag shika nai Akuyaku Reijou ni Tensei shite shimatta...
Isekai De "kuro No Iyashi Te" Tte Yobarete Imasu
Peerless Alchemist
Kumo desu ga, nani ka?
Seijo no Maryoku wa Bannou desu
Ummm, tsura if I dosent bother u can u recommend me mangas with rebirth where the Mc is not too stupid or too cold(⊙…⊙ )