'Cold War' is the latest instalment penned by Mark Gatiss, and features The Doctor and Clara (Jenna-Louise Coleman) facing off with an Ice Warrior aboard a Russian submarine.
Cunningham - who plays Captain Zhukov - told Access Hollywood this week that he greatly enjoyed seeing Smith embody the role of the Eleventh Doctor.
"Matt Smith is a wonderful Doctor. He's wonderful," Cunningham declared, adding: "He's a very quirky character both in real life and as Doctor Who."
The actor continued: "I'd seriously say, I think he's gonna go down as - definitely one of the classics of the Doctors, definitely, definitely, and a delightful human being - as is Jenna-Louise."
Cunningham is well known for his portrayal of Davos Seaworth in Game of Thrones, which kicked off its third season last weekend in the US.
His casting in 'Cold War' came alongside David Warner, Tobias Menzies and Spencer Wilding.
This episode will also mark the first appearance of an Ice Warrior in Doctor Who since 'The Monster of Peladon' in 1974.
Doctor Who airs on Saturday on BBC One in the UK and BBC America in the US.
Doctor Who - 'Cold War' in pictures: