JohnRob:
If you use the SO-8 Surface-Mount device the temperature rise is 150 °C/Watt.
So if your input voltage is 5 volts and you output voltage is 3.3V and your current is 0.280 Amps
Your power dissipated in watts is Pw = (5-3.3)*0.280 = 0.48 watts
I will be using the SOT-23 package, which means 200°C/W, so I will have to decrease the regulator input voltage to 4V, instead of 5V by adding a resistor from the +5V line to the regulator Vin. With the input current being roughly equal to the output current, the resistor needed would be:
Rnominal = 1V / 0.28A ~= 4 Ω, 1/2 Watt
Rmax = 1V / 0.4A ~= 3 Ω, 1/2 Watt
So, choosing a 4Ω 1/2Watt resistor would mean a maximum Pw = 0.7V * 0.4A = 0.28 W power dissipation in the regulator and, thus, 200°C * 0.28W = 56°C junction temperature + ambient with an operating maximum of 125°C. Meaning the regulator would operate safely.
Are my calculations correct? Have I missed anything?