LM7805 vs LM2937 automotive
I saw on some forums that LM7805 dissipate more heat than LM2937, but I didn't have a chance yet to try it.


No, this is nonsense. The LM7805 and LM2937 are both linear regulators; they will dissipate however much heat it takes to drop their input to 5V. Neither part has a significant quiescent current.

The primary advantage of the LM2937 in automotive applications is its hardiness. It can withstand input voltage transients of up to 60V, whereas anything above 35V is likely to destroy a LM7805. These sorts of transients are frequent in an automotive environment, especially when cranking the engine.

Note, however, that the LM2937 has a significantly lower current output (500 mA, vs 1.5 A for the LM7805). This appears to be within your design requirements, but it's worth keeping in mind regardless.