Thompson's chances of taking over in a permanent capacity will have been helped by their rally from conceding an early lead, with Thomas Ince grabbing the winner in the closing stages.
Chairman Karl Oyston is busy interviewing potential replacements for Michael Appleton but Thompson says he will continue to work hard while he remains in charge.
"Until I know anything different, me and my staff will prepare the players. Karl will make the right decision for the club, I've always said that," said Thompson.
"Obviously he's interviewing people, quite a few people, you never know it might get back to me. As staff and players I can't ask for any more than what they are giving us.
"You need to have a team atmosphere and big characters around the place. We needed that, and hopefully that can kick start our season, especially at Bloomfield Road.
"It's nice to score late on in the game at Bloomfield for a change, but we've had to come from behind again. Why are we conceding? It's something we've got to look at, especially the first goal every game.
"It takes a lot of character to keep coming back but it doesn't show a lot of character to concede so it's not a good stat that we want here."