NEW YORK – The back-to-school season got off to a strong start as discounts and high temperatures in July drove shoppers to air-conditioned malls. But merchants worry that momentum won’t continue through the remainder of the second-biggest shopping period of the year as the weather gets cold and the deals dry up.

Despite a flow of bad economic news that kept consumer confidence shaky, a number of retailers reported July revenue Thursday that beat Wall Street estimates, including discounter Target, department store Macy’s, and luxury chain Saks. The International Council of Shopping Centers’ preliminary tally of retailers’ revenue at stores open at least a year was up 4.6 percent, a slower pace than June’s 6.9 percent gain but in line with forecasts.

While the numbers offer encouraging signs for the start to the back-to-school shopping period, which runs roughly from mid-July through September, there are concerns that shoppers will stick to the habits of the Great Recession by focusing on necessities and waiting for sales. That could be a big problem for retailers, who are raising prices in order to offset rising fuel, labor and other production costs.

“Early going, July looks like it’s shaping up to be a solid month despite all the economic headwinds,” said Ken Perkins, president of RetailMetrics LLC., a research firm. “But the concern is whether shoppers will buy back-to-school items at full price.”

The back-to-school season is important for retailers because it accounts for 16.1 percent of annual retailers’ revenue, according to the International Council of Shopping Centers. It’s also an opportunity for retailers to gain insight into consumers’ shopping habits heading into the biggest shopping season of the year, which starts on the day after Thanksgiving.

Retailers will get a better sense of how consumers are spending during the back-to-school season in August, when the bulk of the purchasing is done. But so far, analysts and retail trade groups are sticking to their forecasts for the season, ranging from unchanged to up 3 percent compared with a year ago. The National Retail Federation expects families to spend $603.63 on back-to-school items, from clothing to supplies, down slightly from last year’s $606.40.

“Overall, July sales reports were decent, but the worry is when you look further out over the next three to six months,” said Michael P. Niemira, chief economist at the ICSC. “The growing economic uncertainty may take its toll on future spending.”

The concern among retailers and analysts is that while the recession officially ended in June 2009, many shoppers, particularly in the low-to-middle income bracket, feel like it never ended. For many, wage gains haven’t kept pace with higher household costs for food and gas, which is $1 more per gallon than a year ago. Home values remain depressed, and companies are not hiring.