A 12v adapter will produce about 16v on no load. This voltage drops to 12-13v when the load is 500mA for a 500mA adapter or 1amp for a 1 amp adapter.
If your load is 200mA, the voltage from the adapter will be higher than 12v. It could be about 14v.
If your output from a 3-terminal voltage regulator is 7v, the difference between input voltage and output voltage will be 7v and the current will be 150mA. This produces a wattage of 1watt and this wattage must be dissipated by the regulator. A 3-terminal regulator requires a heatsink when the wattage is above 400mW.