The alliterative American-English phrase a fox in a forest fire—and its usually alliterative extended forms—emphasise the meaning of the adjective that they immediately follow. That adjective usually is hot (used literally or figuratively) or describes agitation, erraticism—here are three examples:

– The adjective hot (used literally)—From Fish Swimming Deep: Smoked Fish Taste Is Difficult to Beat, by Thomas Z. Atkeson, published in The Huntsville Times (Huntsville, Alabama) of Sunday 24^th July 1983:

The weather has us as hot as a fully-furred fox in a forest fire, and the fish are way, way down in the cool depths.

– The adjective hot (used figuratively)—From the column All I Hear Is Here, by John Carter, published in the Daytona Beach Morning Journal (Daytona Beach, Florida) of Saturday 3^rd April 1982:

Hot Dang!—Area country music lovers who enjoyed Ricky Skaggs’ recent appearance here with Ronnie Milsap might be interested in knowing that Ricky’s new single, “Crying My Heart Out Over You,” is hotter’n a fresh flushed fox in a forest fire. Or stronger’n two acres of onions or whatever.

– An adjective describing agitation, erraticism—From Whistle While You Work, But Be Quiet, by Stanton Delaplane, published in the San Francisco Chronicle (San Francisco, California) of Tuesday 5^th April 1988:

In England, a doctor reported gloomily: “The use of alcohol or tranquilizers is necessary for man’s continued existence in this so-called civilized world.”
Man is tense as a fox in a forest fire.

There also exists the phrase like a fox in a forest fire, and extended forms, denoting agitation, erraticism—for example, the following is from the account of an ice-hockey game between the Toronto Maple Leafs and the Calgary Flames, published in the Calgary Herald (Calgary, Alberta) of Sunday 26^th October 1997:

Murphy, discussing the Leafs’ erratic play in the second after taking the lead, said: “We were like a pregnant fox at a forest fire. We were running around everywhere.”

The texts containing the earliest occurrences that I have found of a fox in a forest fire indicate that this phrase originated in sporting parlance:

1, 2 & 4-: From the column Today’s Sports Parade, by Henry McLemore, United Press Staff Correspondent, published in many U.S. newspapers:

1-: On Saturday 14^th November 1931—for example in The Pomona Progress-Bulletin (Pomona, California):

Athens, Ga., Nov. 14 (U.P.)—[…] It’s hotter than a fox in a forest fire down here. I’ll swap you my raccoon coat for a palmetto leaf fan.

2-: On Monday 14^th November 1938—for example in The Grand Rapids Press (Grand Rapids, Michigan):

I have seen many an enthusiastic football follower in my day, but the Tennessee ladies and gentlemen who turned Nashville into an incorporated madhouse Saturday after the Volunteers had kicked Vanderbilt 14 to 0, were the tops in football fanatics.
They had a pretty good excuse, too, because the Tennessee team of the year 1938 is something to behold when it turns on the power as it did in the fourth period against Vanderbilt. I haven’t seen the unscored on, untied, unbeaten Dukes, or the wild-scoring Texas Christians, but if they are any better than the Volunteers they’re hotter than a feverish fox in a forest fire.

4-: On Wednesday 2^nd August 1939—for example in the Mount Carmel Item (Mount Carmel, Pennsylvania):

New York, Aug. 2 (U.P.)—This is the time of year when a man, if he has even one touch of the humanitarian in him, should concoct at least one hot weather hint for his fellow-sufferers under the sun.
I read all the hot weather hints avidly and practice most of them. My hats are filled with leaves and dry ice; I eat all the prescribed hot weather menus and relax completely every 10 minutes no matter where I am. But I continue to be hotter than a fox in a forest fire.

3-: From Sooners Fold Under Man-Killing Power Of Tennessee Crew, the account by H. L. Nations of a football game, published in The Chattanooga News (Chattanooga, Tennessee) of Tuesday 3^rd January 1939:

Cafego took McCullough’s punt on the Sooner 43 and sliced along behind his interference to the 27. His run resembled that of a feverish fox in a forest fire.

5 & 6-: From the sports column Second Guess, by Ned Cronin, published in the Daily News (Los Angeles, California):

– Of Friday 22^nd December 1939—the following is about the forthcoming golf tournament at the Los Angeles Country Club:

The record for the Los Angeles open is 273 and was established by Jimmy Thomson over the Griffith Park course in 1938, when he was hotter than a fox in a forest fire.

– Of Thursday 25^th January 1940—the following is from a list of professional golfers ranging from lightweights to heavyweights:

Right up at the top of the list would be Ralph Guldahl, the big Texan who twice has held the national open title. Clayton Haefner is another heavyweight who currently is hotter than a fox in a forest fire.

7-: From the column Top O’ The Mornin’, by Christian and Ashford, published in The Lexington Leader (Lexington, Kentucky) of Sunday 10^th March 1940:

Captain Rouse, who was voted a place on the All-Southeastern Conference first team, became as hot as a feverish fox in a forest fire in the second half of the Wildcat-Mountaineer battle, dropping in four long shots.