which datasheet and which package? The national one
http://cache.national.com/ds/LM/LM117.pdf
has lots of packages. K is the TO3 package and has a junction to ambient (Ja) of 35. T is the TO220, with a Thetaja of 50
By the way, your voltage drop is 1.72, not 2.72. not exactly good news for non thermal reasons
Your conclusion is correct but I'm suspicious of the 19C/W number. A TO3 should outperform the TO220 but the the national datasheet says the TO3 is 35. Using 1.72V, you'd get .344 watts. .344 * 50 is about 17.2C so you are looking at 42.2C. (they use ambient of 25C) No heat sink needed.
bad news, the LM317 is not a low dropout regulator. Look at the the chart for drop out voltage. I think it shows 200 mA as right on the line for around 1.7V. It's pretty close and you might get away with it but if you push the current up at all, you will have a problem. Interestingly enough, the dropout voltage goes down as the temp goes up.
There are several LDO linears that will work for you. In through hole there is the LD1117 from ST and national LM2937-3.3. both are fairly cheap. There are a lot of SMT parts that will do this as well.