U.S. crude for June delivery rose $1.07 to $125.19 a barrel by 0934 GMT, within sight of its record peak of $126.98 hit earlier this week.
July ICE Brent was $1.22 higher at $123.85 a barrel.
"Global supply of distillates is very tight," said Tetsu Emori, fund manager at Astmax Co Ltd in Tokyo.
Surging demand from developing countries, such as China, is helping bolster heating oil prices. PetroChina is seen buying a third more diesel at 400,000 tonnes for June versus May's levels, following a deadly earthquake that has cut supplies of natural gas-generated power.
Thin gas oil stocks in Northwest Europe caused by a string of refinery outages have also prompted players to scramble for Asian barrels.
NYMEX June heating oil was up nearly 0.5 percent at $3.6435 a gallon, off highs of $3.6615 which brought it near its record high of $3.7228 hit on Wednesday.
The dollar weakened against the euro, adding to Thursday's losses after data showing U.S. industrial production fell 0.7 percent in April, the biggest drop in the manufacturing sector since September 2005.
Oil and the U.S. currency have become closely intertwined in recent months as investors have turned to oil as a hedge against the falling dollar.
BUSH IN SAUDI
U.S. President George W. Bush lands in Saudi Arabia on Friday to renew his appeal for the world's biggest producer to help tame record oil prices.
Saudi Arabian Oil Minister Ali al-Naimi oil minister reiterated on Thursday the view of OPEC's biggest producer that prices had more to do with financial market volatility than fundamentals.
OPEC smallest producer Ecuador said the group should consider raising output because record high prices are hurting poor nations.
"I think OPEC has to deal with this issue, because this is hitting all the poorest countries that are oil importers," Ecuador's President Rafael Correa told Reuters in the Peruvian capital, Lima.
OPEC's own Monthly Oil Market Report provided more evidence that record oil prices are slowing demand growth. It lowered its forecast for 2008 world demand growth to 1.16 million barrels per day, 40,000 bpd less than its previous forecast.
The all-rounder hammered an unbeaten 104 off 48 balls to secure a five-wicket victory for Australia
UAB offers special rates and benefits for its environmentally-cautious retail customers
AWNIC maintains a robust financial stance, boasting exceptional capital adequacy