Once you have confirmed the pipe is frozen but not burst, open the faucet connected to that drain. This relieves pressure in the system and gives the melting ice a path to escape.
Here are some effective methods for thawing a frozen drain pipe: how to thaw a drain pipe
If heat and hot water aren't working, the ice may be too dense, or there may be a grease clog accompanying the ice. Once you have confirmed the pipe is frozen
A frozen drain pipe is a hassle, but it is a manageable one. By acting quickly and using gentle heat, you can protect your home from water damage and keep your plumbing flowing all winter long. A frozen drain pipe is a hassle, but it is a manageable one
If the frozen section is visible (e.g., under a sink or in a basement), use a hair dryer on a low to medium setting. Start at the end closest to the drain and work your way toward the blockage to allow melted water to escape.