I have two Esp8622-01 modules one with firmware V0.40 and one with V0.60, both have the same problem.
When I send the AT command in order to change the baudrate fx. AT+UART=115200,8,1,0,0 (the value of the baud doesn't matter - any baudrate)
The baud rate is changed, so long, so good, but the current draw increases from 70mA to 120 mA (a factor 1.7)
The Only way to get back to 70mA again, is to send the factory restore command AT+RESTORE.