The 45-year-old actress, who was pictured arriving in Cape Town to film scenes for the Amazon series back in January 2018, told the Daily Mail that the stifling heat took its toll on her.
"It was incredibly hot - so hot that I ended up getting taken to the hospital one day for passing out," she recalled. "I just keeled over into this very nice, huge actor, which was lucky. Friend for life!".
Kate didn't name the actor she fell into, but she co-stars in the series with Babs Olusanmokun, Jacky Ido and Matthew Gravelle. Charles Dance and Alex Kingston also feature.
After recovering following her hospitalisation, Kate got back to filming. But when she wasn't required on set, the screen star made the most of the local wildlife, and enjoyed going on regular safaris.
Recalling one particularly memorable moment, Kate smiled: "I brushed a lion with a hairbrush at one point; he was chilling."
While it seems to be unrelated, Kate also found herself being rushed to hospital last month, when an ovarian cyst exploded.
The British actress revealed she was in tears as she was given morphine to alleviate the pain after her terrifying ordeal.
"Turns out a ruptured ovarian cyst really hurts and morphine makes me cry," she captioned a snap of her crying in a hospital bed on Instagram. "So thankful to everyone who looked after me #wobbly."
Kate is seen in the picture with an oxygen tube up her nose, and another snap showed her curled up on the bed in pain.
She's now believed to have fully recovered from the health ordeal, and put on a stunning display in a dramatic black and gold gown as she arrived at the Vanity Fair Oscars party on Sunday night.