Here is the spec sheet on the diode I have from ebay. Looks really close to yours.
Also I did a really fast thermal test.
I set the diode at .35a and that worked out to 100mw after about 30min of warm up time no tec. The temp stabilized at 100f.
Then I turned on the tec and plotted the power after about 10 min.
At it's min temp it was 73F and 135mw. I then turned the tec off and let it warm back up. It came back down to 99mw and 102f probably a little warmer because of the thermal mass of the hot side of the tec.
SO these really like to be cold. blue laser diode 004.pdf
445 temp vs power.PNGCapture of data.PNG
When the going gets weird, the weird turn pro.