Why is my pizza dough sponge failing?
Might be temperature, might be technique. While the dough will proof faster at the optimal temperature, you can also proof it for longer. Some recipes proof the dough in the refrigerator (See Using low oven temperature to accelerate proofing). So you can compensate for a lower temperature by extending the proofing time.

Technique is also important. I don't know why you split the process into 2 parts, but my guess is adding the salt without a buffering agent is killing off the active yeast. 

I have had a lot of success with no-knead recipes, which you can modify if you prefer to knead your dough. Add your flour to the bowl, 1 Tsp salt and mix well. Add your yeast (1/4 Tsp packet or bread machine yeast), and mix well. If desired you can add sugar and some olive oil. Add your blood temperature water (~ 38C) a 100ml at a time, reducing the quantity towards the end. You want add sufficient water to hydrate the flour until it just comes away cleanly from the bowl. Your dough is ready to be proofed when it just comes together and is neither too sticky or too dry. You can then cover and proof for between 2 - 18 hours or until it doubles in size. You can tell by the "stringiness" of the dough how well it has proofed.