The coolest Republican is Adam Kinzinger - who most of the party considers to be a RINO...
On the other hand, the most beloved figure in the party is a twice-impeached ex-president who was so bitter about his loss he refused to expect it and tried to have his cult invade the capitol of his own country. Less cool, and more concerning/disturbing/psychotic.
Adam Kinzinger might be one of the most uncool people in America, and by-and-large, only uncool people would know who he is. The only uncool-er person in the Republican Party may be formerly cool Rudy Giuliani with his hair dye dripping down his temples. AK's just the flip side of MTG's uncool-factor.
The "cool" factor in the Trump administration probably begins and ends with Anthony Scaramucci.