* High inventories, record production limit price gains * Warm up late this week, next week keeps buyers cautious * Coming up: EIA, Enerdata natgas storage data Thursday By Eileen Houlihan and Joe Silha NEW YORK, Feb 6 (Reuters) - U.S. natural gas futures ended higher on Wednesday for a third straight day, backed by expectations that heating demand will pick up when another shot of cold moves into the Midwest by late next week and then spreads east. "Some short-term forecasts look a little more supportive, but winter is almost over, and the probability of extremely cold weather is diminishing every day," said Tom Saal, senior vice president at INTL FCStone in Miami. Front-month gas futures on the New York Mercantile Exchange ended up 1.9 cents at $3.418 per million British thermal units after trading between $3.398 and $3.459. The nearby contract, which hit a 6-1/2-week high of $3.645 two weeks ago, has gained 3.5 percent in the last three sessions following a 4.2 percent slide last week. While gas prices have tried to rally this week since last week's low in the $3.20 area, traders noted that the move up has been difficult, with inventories still relatively high, production flowing at or near a record peak and another brief warm up expected next week that should again slow demand. Commodity Weather Group on Wednesday said next week's warming was a bit weaker overall with computers models in better agreement on colder risks, particularly in the 11-to-15-day outlook. Chart traders said the technicals turned neutral this week as the front month contract broke minor resistance at the 40-day and 100-day moving averages on the way up, but most agreed it would take a close above the $3.645 high from two weeks ago to turn the trend bullish. BELOW AVERAGE STORAGE DRAW EXPECTED Traders and analysts polled by Reuters expect inventories to have fallen by 132 billion cubic feet (bcf) last week when the U.S. Energy Information Administration releases its weekly storage report. Stocks fell an adjusted 94 bcf during the same week last year. The five-year average decline for that week is 165 bcf. Inventories have dropped 7 percent below last year's record highs at this time, but are still relatively high at 304 bcf, or 12 percent, above the five-year average. If drawdowns for the rest of winter match the five-year average, inventories will end March at 2.032 tcf, about 18 percent above normal, but 18 percent below last year, when stocks finished a mild heating season at a record-high 2.48 tcf. PRODUCTION FAILS TO SLOW DESPITE RIG DECLINES Baker Hughes data on Friday showed the gas-directed drilling rig count fell last week for the third time in four weeks, dropping by six to 428. While the gas rig count is hovering not far above the 13-1/2-year low of 413 hit three months ago, production has shown no significant sign of slowing. The U.S. Energy Information Administration estimates that marketed gas output in 2013 will rise slightly from 2012 levels, the third straight yearly record.