* New front month well below recent 21-month high * Above-normal temperatures on tap but not extreme heat * Nuclear power plant outages back below normal * Coming Up: Baker Hughes drilling rig data Friday By Eileen Houlihan NEW YORK, May 30 (Reuters) - U.S. natural gas futures were lower for the fourth straight session on Thursday, tumbling nearly 4 percent on the day and nearly 6 percent this week, as forecasts for milder weather and slack nuclear plant outages weighed on sentiment. Neutral weekly inventory data also did little to impede declines, traders said. "From a fundamental perspective there is less nuclear outages compared to both last year and the five-year average, and as such the call on natgas to supplement nuclear power generation is less than the historical data, suggesting that the upcoming inventory injections are likely to over perform," said Energy Management Institute's Dominick Chirichella. He added that the latest temperature forecasts were less supportive than those issued earlier in the week. "Based on the latest forecast it does not appear that there is going to be a surge in natgas cooling-related demand anytime soon," Chirichella said. Front-month July natural gas futures on the New York Mercantile Exchange slid 16.1 cents, or 3.85 percent, to settle at $4.023 per million British thermal units. The nearby contract traded between $4.011 and $4.184, trading in the $4.13 area just prior to the release of U.S. government storage data at 10:30 a.m. EDT (1430 GMT). The contract is down nearly 6 percent in the past four sessions. The spot contract hit a one-month low of $3.883 on May 9 after climbing to a 21-month high of $4.444 on May 1. Other months ended much lower as well, with the August contract falling 16 cents, or also nearly 4 percent, to end at $4.043. Winter months lost about 14 cents each. Data from the U.S. Energy Information Administration showed inventories rose last week by 88 billion cubic feet, in line with Reuters poll estimates, but above the year-ago build of 72 bcf. Stocks have gained 92 bcf on average that week over the past five years. Stocks, at 2.141 trillion cubic feet, are 664 bcf, or nearly 24 percent, below year-ago levels. They are also 88 bcf, or nearly 4 percent, below the five-year average. In the cash market, gas for Friday delivery at the NYMEX benchmark Henry Hub in Louisiana slid 3 cents to $4.12. Early deals eased slightly to 4 cents under the July contract, from those done late Wednesday at a 3-cent discount to the June contract. Gas on the Transco pipeline at the New York citygate , however, jumped 28 cents to $4.92 on some late week heat in the Northeast. The latest National Weather Service six- to 10-day forecast issued on Wednesday called for above-normal temperatures in the western third of the nation, in the Northeast and much of the Midwest, and mainly normal readings elsewhere. Nuclear plant outages totaled 13,600 megawatts, or 16 percent of U.S. capacity, down from 15,700 MW out on Wednesday, 17,400 MW out a year ago and a five-year average outage rate of 14,400 MW. Traders awaited the next Baker Hughes gas drilling rig report to be issued on Friday. Last week's report showed the gas-directed rig count was unchanged at 354. The count posted an 18-year low of 350 three weeks ago.