The force has urged people to only call 999 in emergencies.
A spokesman for the WYFRS said: "Our 999 Service is currently experiencing a significant increase of calls due to the warm weather.
"Please remember to only dial 999 in an emergency.
"This should help allow genuinely urgent calls to be promptly answered."
Both the fire service and West Yorkshire Police have been vocal on social media about the dangers of the hot weather and open water.
They said: "It might be warm, but cooling off in open water can have deadly consequences. Please don't enter open water. (If you are out and about & see somebody struggling in water, call 999 and ask for the Fire Service. We have the training and equipment to help.)"
Temperatures in Leeds will hit a scorching 27C this weekend, according to the Met Office weather forecast.
Saturday is a very hot day, with less cloud and the mercury hitting 27C by mid-afternoon.
The Met Office weather outlook for Saturday to Monday said: "Fine and dry with plenty of sunshine on Saturday and Sunday.
"Feeling very warm, with light winds. A bright start on Monday, but perhaps turning cloudier from the north later."