Even as the weather turns cool, the prospect of a “Didi hot” wave lingers around the Yankees.

Whether it ever fully arrives in 2019 could determine the future of the Yankees’ shortstop position.

Didi Gregorius contributed a three-run homer to the Yankees’ 10-1 shellacking of the Rangers on Tuesday night at Yankee Stadium, another highlight in what has been a decidedly uneven year for the impending free agent. Other big hits from the ultra-popular veteran have prompted manager Aaron Boone to publicly wish for what he calls a “Didi hot” streak, one of Gregorius’ torrid runs at the plate that we’ve witnessed in past seasons.

Maybe this round-tripper, Gregorius’ 14th of the year, will serve as the spark. Or maybe it will turn into another false alarm.

Following this Yankees win, in which James Paxton twirled a seven-inning, one-hit, one-walk, 12-strikeout gem, Gregorius owns a modest .253/.285/.466 slash line, the first two rates his lowest in five years as a Yankee, as well as defense beneath his typical standards.

“I haven’t really [taken] off yet,” Gregorius acknowledged to The Post before the game. “Everybody knows I had Tommy John [surgery, on his right elbow, last October]. I’m coming back from that. I’m not making it as an excuse, but I’m not where I want to be yet. It takes time.

“But as far as where I’m at right now, I’m still unhappy with it. I still feel like it should be way better.”

Only the least forgiving talent evaluator would ignore the reality of what it means to return from the Tommy John procedure, even for an infielder. And maybe that benefit of the doubt will prove enough to get Gregorius the big contract for which he has worked his entire career. Something comparable to, if not quite matching, the six-year, $120 million package Xander Bogaerts signed with the Red Sox this season. Gregorius’ average exit velocity of 87.6 miles per hour through Monday’s action marked his best in the Statcast era, an encouraging sign.

Or perhaps Gregorius will fall victim to the industry’s not trusting anyone over 30; he’ll turn 30 next February. His increased strikeouts (40) and decreased walks (11) sound an alarm. Throw in the fact that many big-market teams — the Red Sox (Bogaerts), the Astros (Carlos Correa), the Dodgers (Corey Seager), the Nationals (Trea Turner), the Phillies (Jean Segura), the Mets (Amed Rosario), the Cubs (Javier Baez) and the White Sox (Tim Anderson) — already employ a good shortstop.

Which is why, as things stand now, Gregorius stands as an interesting candidate for a free-agency rarity: Accepting the qualifying offer. Taking a year to reboot and put forth your best self. And, because players can receive the qualifying offer only once, shedding draft compensation for your next free agency.

Last November, only one free agent — the Dodgers’ Hyun-Jin Ryu — accepted the one-year, $17.9 million qualifying offer. He had made only 18 regular-season starts totaling 82 innings in the 2018 regular season plus four postseason starts, limiting his market. This season, as a top candidate for the National League Cy Young Award, Ryu has positioned himself more robustly.

Gregorius, who hit a grand slam off Ryu on Aug. 23 at Dodger Stadium, possesses time to render this issue moot.

“I still feel like it’s in there,” Boone said before the game, of a “Didi hot” run. “Hopefully over this final month, he can build up momentum and go into what we hope is the postseason physically in a real good place.”

Nathan Eovaldi, Gregorius’ Yankees teammate in 2015 and 2016, showed last October what a strong postseason can get you, as the Red Sox rewarded him with a four-year, $68 million extension. Gregorius’ reputation as a good teammate and a fun social-media presence will only help his cause, and as well as Gleyber Torres handled shortstop in Gregorius’ absence this year, do you really think the Yankees should jettison him — and the accompanying roster depth — now?

After the game, a smiling Gregorius said, “Hopefully sooner than later” when asked about a blast-from-the-past roll. Either way, the best forecast, this far out, calls for Didi to stick around The Bronx at least a little longer.