The good news for you sizzling 49ers fans is that your team has realized that its stadium, The Kitchen, has a heat problem. On sunny days, half the fans are fully baked, and that’s not a pot reference.

The not-so-good news is that the 49ers, now searching for solutions, might be closing the barn door after the rooster got a sunburn, or whatever that old farm expression is.

According to one expert, an architectural engineer with extensive experience building sports venues, the 49ers blew it by not addressing the sun issue when they designed Levi’s Stadium.

“Gosh, it’s just such a missed opportunity for them,” said the expert, who requested anonymity. “We do buildings where we do ‘thermal-comfort analysis.’ It’s a very robust computer model that looks at all environmental aspects to determine what the comfort level is inside the building. It would have been so easy to have done that and find out: ‘In the fall months, you have no wind, and the sun is beating down on you, here’s how it’s going to feel.’

“They made a decision to say, ‘All right, fine, we’re going to let those (fans) bake,’ and that’s what happened.”

Temporary solution: Play at night, like Thursday’s game against the Rams. But day games? Problem.

Did the 49ers and their stadium-builder, HNTB, conduct computer-climate studies? If so, did they ignore them to save money? I asked Lanson Nichols of HNTB, who was involved with the planning.

“One of the things that was primarily important to the fans, as well as the team,” Nichols said, “was that this be an open-air stadium: natural-grass field, the essence of football being played outdoors. It was never really a mandate to do a roof. You don’t normally do those kinds of (computer) comfort studies.”

Nichols said weather studies were done, but not the specific kind of computer analysis to which the stadium-building expert referred, because that’s not a study HNTB normally would do for an outdoor stadium.

“So no, it wasn’t really a question that was asked — ‘Is this going to be uncomfortable?’ — because that’s kind of a normal condition in an open-air stadium,” he said.

Nichols speculated that 49ers fans grew accustomed to Candlestick’s chill and have been slow to adapt to the breeze-free sunshine at Levi’s.

Are 49ers fans wimps? It’s hot at the Oakland Coliseum and in Tuscaloosa, but fans there don’t scurry for shelter. Nah. Niners fans aren’t that wimpy. Candlestick could bake on September afternoons.

There is an element of mystery here. Maybe this is a freakish hot spot. Maybe a computer-model study would have shown, Damn, it’s going to be like sitting under a magnifying glass!

The cold reality: It’s a problem. And any structural fixes now would be major, my source said.

“It would have to be a huge, beefy structure,” he/she said, referring to any type of shade or roof. “I think it’s a huge lift. You just can’t put anything up that is going to weather the storm and be structurally sound under our seismic conditions.”

Lightweight plastics and panels that could be used for shades, but they require steel supports.

“So I think it would be hugely disruptive and very costly to get anything up that really addressed the issue there,” the expert said.

The guesstimate? Hundreds of millions of dollars to throw a little shade on the sun-assaulted east siders.

In fairness to 49ers CEO Jed York, who — with sidekick Paraag Marathe — hustled up the financing for the stadium, it was a scramble to raise all that dough, so maybe this was simple economics; Jed and family couldn’t afford shade. If so, I wonder if the Yorks now wish they had cut corners elsewhere — fewer ritzy frills — and diverted the money to shade.

“I think it was a cost-saving issue,” the architecture expert said, purely speculating. “They simply did not want to do a stadium that was domed or had any kind of shading device. ... The 49ers are going to suffer for years and years to come because of that poor investment decision.”

I could have helped the 49ers. When the stadium was being built, I tried to arrange a tour of the construction site for my feng shui expert, Deborah Gee, a global authority on the ancient Chinese art of harmonious flow of life force, or chi.

Gee knows her chi. In 1999, she and I toured the Giants’ under-construction ballpark and Gee predicted great things for the Giants there. She even provided a rough timeline for their success.

Gee and I had to wait until Levi’s was finished to do our feng shui inspection, so it was too late to warn the Yorks that they had a sun problem.

Gee liked most of what she saw, but, as I wrote then, “It concerned Gee that there is little or no shade for the fans, except for the fat cats in their luxury caves. Sure enough, three days later (at the first game), the sun and 80-degree temperature drove many fans to first-aid stations and sucked thousands more out of their seats to shady concourses or indoor clubs. It was a crummy game, too, but the grandstands became deserted in the second half.”

I asked Gee if the 49ers could do anything to fix the flaws.

“There are remedies,” she said, “but they are not to be shared indiscriminately, only with those who listen with sincerity in their hearts.”

The 49ers chose not to open their minds and hearts to Gee.

The sun isn’t the only problem. The team is not stellar, and the under-the-grandstands VIP Tequila bunkers lure fans into air-conditioned luxury.

But the sun, she is a problem.

My architectural source has attended several games at Levi’s, but has sat in the luxury boxes on the cool, shaded west side.

“Looking down on the seats facing east,” the source said, “it looks pretty miserable over there. It’s the haves and the have-nots, and they’re just over there baking, paying a couple hundred bucks to just roast.”

The 49ers bought the steak. Now they’re dealing with the sizzle.

Scott Ostler is a San Francisco Chronicle columnist. Email: sostler@sfchronicle.com Twitter: @scottostler