A modified car often based on a 30s-50s Chevrolet or Ford (mostly Ford) that is modified with characteristic visual upgrades (wide tires, exhaust pipes etc)
When a person eats a spicy pepper and proceeds to suck another person's dick. The penis reacts with the peppers, making it red and blistered, hence the name hot rod
Besides its well-known meaning, "an automobile that has been rebuilt or modified to increase its speed and acceleration", "hot rod" also means a person who drives a really cool car but who is too ostentatious.
From "10 Things I Hate About You":
Walter Stratford: I know who you wanna bend the rules for. It's that hot-rod Joey.
Bianca: What's a hot rod?