Cole left West Ham in the summer following seven years at the club, but the Hammers handed him a short-term contract in October after the severity of Andy Carroll's injury became clear.
The 30-year-old started repaying manager Sam Allardyce on Saturday afternoon when he came off the bench to score the second goal in West Ham's 3-0 victory over Fulham.
The former Chelsea man now hopes he can start banging the goals in on a regular basis.
"Once you score you feel you can get in a rhythm and score more so hopefully there will be more to come for me now," said Cole, who drew a blank in the first four games since he re-signed for the club.
"Hopefully they will be important goals. I want to keep the momentum and doing the right thing."
Should he keep scoring, Cole admits his chances of prolonging his stay beyond January, when his contract expires, will improve.
"I want to stay, of course, and I'm very confident," he said.
"I know the ins and outs of the club. Sometimes change is good but I'm here and have been here for so long - I'd like to stay on.
"It's up to the manager. I can only play my best and try to play to my capacity on the field. Whatever they will do in the future is beyond my control.
"We'll see how it goes. I'm fit now, I've always been working for my fitness and the manager has been waiting for the right time for me to start.
"Hopefully I've done myself a favour and will get a start soon. I'll wait for the manager to make the decision."
Fellow substitute Joe Cole and Mohamed Diame were also on the scoresheet in what turned out to be the Hammers' first home win since the opening day of the season.
The Hammers fans who booed their team off after last week's 3-0 win over Chelsea lauded their team on Saturday afternoon.
But given that West Ham are still only three points above the relegation zone, Cole knows his team cannot afford to take their foot off the accelerator.
"We saw the Fulham game and the Crystal Palace game (on Tuesday) as six-pointers," Cole added.
"So the next game is another big game for us.
"Hopefully we can get our first back-to-back wins of the season.
"We're doing our match preparations now, we're ready."