Bowyer, assisted by head of youth Terry McPhillips, has stepped up from his reserve team duties following the departure of Henning Berg after just 57 days in charge.
The pair have since led Blackburn to victories over Barnsley and Nottingham Forest and the club announced on Thursday that they would remain in charge for the rest of the month.
However, Bowyer, who has refused to rule himself out of the running for the permanent job, admits they may not last that long.
"We've been told until the end of January but we're not daft," said Bowyer. "We know that if it doesn't go particularly well for us that could change.
"We'll just keep doing what we've been doing and hopefully we can continue the success that we've had.
"It would be naive of us to to say 'yeah we definitely want it' and it would be naive of us to say 'no we don't want it'.
"I know it's a bit of a cliche but we'll just going to keep doing what we're doing, hoping to buy the club a bit more time."
Of the extended tenure granted to himself and McPhillips, Bowyer added: "I think it's a ringing endorsement of the players and the way they've gone about it in the last couple of games.
"The players have taken full responsibility for their levels of performance. We can only control what we can control.
"There's a lot going on at the club but we've just told the players to concentrate on their football and they've been magnificent.
"We've had a bit of luck with the first goal in each game and from that the players have gone and performed.
"They take confidence from the hard work and commitment they've put in."