* Weather outlook turns cooler for Midwest * Nuclear power plant outages climb back above average * Coming up: EIA monthly gross gas production data Tuesday By Joe Silha NEW YORK, April 29 (Reuters) - U.S. natural gas futures ended up sharply on Monday after losing ground last week, underpinned by expectations for another light weekly inventory build on Thursday and cooler late-week weather forecasts for the Midwest that should stir more heating demand. Cold late-winter weather, a chilly spring and above-average nuclear plant outages put a huge dent in record gas inventories and helped drive up gas price expectations for this year. "The June contract is moving higher today in response to colder updates to the weather forecasts. Traders are now pricing in the possibility of a very limited (spring) shoulder season," Gelber & Associates analyst Aaron Calder said in a report. Gas prices, pressured last week by technical selling after nine straight weekly gains, slid nearly 6 percent as new longs in the market opted to take profit ahead of milder weather expected in May that should slow space heating needs. Traders also noted that gas prices over $4 were likely to curb demand by prompting more utilities to use coal rather than gas for power generation and increase supply by encouraging producers to turn on more wells. Front-month gas futures on the New York Mercantile Exchange ended up 16.9 cents, or 4 percent, at $4.392 per million British thermal units after trading between $4.225 and $4.395. The front contract, which hit a 21-month high of $4.429 on April 18, last week posted its first weekly decline in 10 weeks. The slide broke trendline and moving average support, but most chart traders were not ready to call an end to the bull market, which began in mid-February and had driven futures up some 40 percent. Most were waiting to see if the new front contract can hold above $4 when milder spring weather arrives. While Commodity Weather Group expects the Midwest and South to cool again later this week, the forecaster said the East Coast should continue to see low demand, with no significant warming or cooling loads expected for the next two weeks. ANOTHER LIGHT INVENTORY BUILD EXPECTED Data from the U.S. Energy Information Administration last week showed total domestic gas inventories rose by 30 billion cubic feet to 1.734 trillion cubic feet. That was below the Reuters poll estimate of 32 bcf and well below the five-year average increase of 50 bcf for that week. The stock-building season got off to a slow start this year, with only two injections reported so far after an unusually cold spring forced homeowners and businesses to turn up their heat. Inventories now stand at about 807 bcf, or 32 percent, below last year's record highs at this time, and 94 bcf, or 5 percent, below the five-year average. Early injection estimates for Thursday's EIA report range from 24 to 40 bcf versus a 31-bcf build a year earlier and a five-year average rise for that week of 67 bcf. OUTPUT NOT SLOWING MUCH YET Baker Hughes data Friday showed the gas-directed rig count fell last week by 13 to a 14-year low of 366. The count had risen slightly in the two previous weeks, but the latest drop likely eased concerns that the recent surge in gas prices had prompted producers to bring on more supply. Drilling for natural gas has mostly been in decline for the past 18 months, but production so far has not slowed much, if at all, from the record high hit last year. EIA on Tuesday will release data on gross natural gas production in February after reporting slight declines in the previous two months.