Gary Simpson, 43, was batting for his Yorkshire club when he complained of feeling thirsty and unwell during his team's away match at the weekend.
Mr Simpson collapsed a short time later and died in an ambulance on the way to hospital. It is not yet known whether the temperatures, which reached 25C on Saturday, played a part in his death.
His daughter Charlotte, who plays at New Farnley Cricket Club, in Leeds, the same one as as her father, said: "He will be so sadly missed, he was loved by everyone at the club and such a big part of of it. It is such a shock he is gone. "
She captained the New Farnley C team on Sunday as a tribute to her father. Yesterday, Charlotte, 21, said: "It's what he would have wanted, he loved cricket and got me into it. He would have liked it and he was there with me all through the day."
Chairman John Baldwin said: "Gary was a popular member of the club who played for the club all his life, coming up through the juniors.
"All his family, including his brother, father and daughter, either played for the club or umpired for the club and are interwoven into the fabric of the club.
"It's a very distressing time for all at the club but Gary would not have wanted to go any other way than out in the middle while batting for his team."
Mr Simpson's team, New Farnley A, is the club's second team and is seventh in the Third Division of the Central Yorkshire Cricket League. They were playing Wakefield St Michael's on Saturday when he collapsed.
Mr Simpson's brother, Andrew, another long-term member of the club, said yesterday his brother "had no history of illness" and the family did not yet know what caused his death.