* Never be too confident about price stability - Yergin

* Heavy-hitters from govt, industry to attend CERAweek

* Themes include demand recovery, climate change

HOUSTON, March 5 (Reuters) - Oil company executives should not get too complacent about how oil prices settled in the $70-$80 a barrel range over the last several months as the economic recovery has yet to catch up, the head of consultancy IHS Cambridge Energy Research Associates IHS.N warned ahead of the CERAWeek conference next week.

While crude appears to have found a sweet spot, the global recession has eroded demand for gasoline and diesel, and Washington wants to regulate the carbon-intensive energy industry’s emissions.

And after two straight yearly declines in global oil demand took prices from their 2008 heights near $150 a barrel to about $32 in December 2008 before recovering to about $80 currently, sure signs of economic recovery that industry officials and government policy-makers crave aren’t quite there.

“One lesson we’ve learned about the oil price - never to be too confident about stability,” said Daniel Yergin, chairman of IHS Cambridge Energy Research Associates and author of the Pulitzer Prize-winning history of the oil industry, “The Prize.”

The symbiotic link between oil and the economy will dominate CERAWeek, the prestigious consultancy’s annual go-to gathering of elite energy and economic figures and thinkers, which begins Monday in Houston.

Every year, CERA gathers top executives from the world’s dominant energy players, from publicly traded and state-owned oil and gas companies, global oilfield services providers and major utilities to bankers, economists and government leaders.

This year's gathering has a particularly international flair, with leaders of state oil giant Saudi Aramco [SDABO.UL], Russia's Gazprom GAZP.MM, Brazil's Petrobras PETR4.SA and Norway's StatoilHydro STL.OLSTO.N.

Top executives for the third-largest U.S. oil company, ConocoPhillips COP.N and the largest U.S. refiner, Valero Energy Corp VLO.N, will also attend.

The lineup also includes the U.S. Secretary of Energy Steven Chu, assistant to President Barack Obama for economic policy Larry Summers and International Energy Agency Executive Director Nobuo Tanaka.

In the grips of a global recession, energy companies largely hunkered down, canceled or delayed projects, cut costs and fired thousands of employees. Weak demand and anemic margins prompted some refiners to shutter plants.

But as oil prices crept up, deal flows began to thaw with well-heeled giants carefully choosing deals that boost reserves or capabilities. Those include Exxon Mobil Corp's XOM.N $27 billion acquisition of onshore natural gas producer XTO Energy Inc XTO.N announced in December and oilfield services leader Schlumberger Ltd's SLB.N announcement last month of plans to buy rival Smith International SII.N for $11 billion.

“People have been feeling more confident about the price for a while now, and they feel they can go ahead,” Yergin said.

Panel sessions and speeches throughout the conference will focus on prospects for further consolidation as oil majors struggle with boosting reserves; how and where oil demand will grow, particularly in China and other emerging economies; the future of demand for gasoline, diesel and other refined products; and the future of unconventional natural gas given vast potential of U.S. shale plays.

U.S. climate change legislation, stalled in the shadow over healthcare reform gridlock, also will be a hot topic as the energy industry is in limbo, awaiting clarity on regulation and cost.

But even though economic recovery is in progress, demand in developed countries remains flat and unemployment in the United States, the world’s largest energy consumer, remains at its highest in a quarter century.

Also, capital costs that skyrocketed alongside oil prices have not ebbed as much as expected, “so that’s a concern for a lot of the industry,” Yergin said.

So oil prices near $80 a barrel reflect economic optimism and hope, Yergin said.

“There’s a gap between expectations and the current realities of supply and demand,” he said. “This is not an oil price reflecting how big the spare capacity is, and how big the inventories are.” (Reporting by Kristen Hays; Editing by Marguerita Choy)