No, there is no soft reset function. In order to reset the bus you will need to send 9 SCL clocks while letting the the SDA line float in order to clear out the buffer.
DS1624
Production
The DS1624 consists of two separate functional units: a 256-byte nonvolatile E2 memory and a direct-to-digital temperature sensor.
The nonvolatile memory...
Datasheet
DS1624 on Analog.com