July 31 (Reuters) -ICE cotton futures rose on Monday and were set to record their biggest monthly gain since January, as a heat wave in the U.S. fanned concerns over supply of the natural fiber.

* The most-active December cotton contract CTZ3 rose 0.33 cent, or about 0.4%, to 84.59 cents per lb by 11:54 a.m. EDT (1554 GMT). It traded in a range of 83.75 to 86.31 cents a lb.

* The contract was up about 5.4% so far for the month.

* "The dry land crop is suffering", as temperatures this week in the delta are going to hit 100 Fahrenheit (37.3 degree Celsius), with no rainfall forecast into next Monday, said Rogers Varner, president of Varner Brokerage, in Cleveland.

* A 1.2% monthly fall in the dollar index .DXY also made cotton cheaper for holders of foreign currencies. USD/

* "The only way for the market to get over the upper 80s is for a surprise weather event such as a hurricane hitting open cotton somewhere in the world," Varner said, adding prices in the near term would be between 85 and 89 cents.

* Sentiment in the cotton market also got a fillip from gains in Wall Street on hopes of a soft landing for a resilient U.S. economy, while cooling inflation fueled bets for a pause in U.S. rate hikes. .N

* Elsewhere, Chicago wheat, corn and soybeans fell as forecasts of milder weather in the U.S. Midwest grain belt eased concerns over heat damage to U.S. crops. GRA/

* Although the forecasts were for less heat than previously expected, the outlook was still for hotter-than-normal weather through mid-August. NGA/

Reporting by Harshit Verma in Bengaluru; Editing by Shilpi Majumdar