The tire manufacturer supplied the teams with slick tires during testing at Jerez last December with the aim of introducing them at the beginning of 2009.
However, many drivers expressed concerns about the difference between the temperatures of the tires when they left the pits compared to when they were at full operating temperature.
This resulted in a variation in lap times of several seconds between cars that prompted safety fears.
The Japanese manufacturer hopes the new range of tire compounds and higher track temperatures will sort out the warm-up issues.
"We are thinking about the compound range at the moment," Hirohide Hamashima, director of Bridgestone's motorsport tire development, said.
"We want to check our warm-up issue, because in the winter time we had a warm-up problem and many drivers complained about the warm-up of the tire.
"It took too long and there was an imbalance, because the rears warmed up quickly. So after two or three laps, the fronts were cold and the rears were hot. So the rears got a little bit tired before the fronts came in, which made it difficult to drive."