SM5100B Cellular Shield Troubleshooting

I have the same SM5100B shield + software using SoftwareSerial class.
I noticed when module receives a SMS, it stops working in case the ambient temperature drops under 2 Celsius.
At the normal temperature (23 Celsius) it works OK.
I think the problem is the power supply (it is under-dimensionated). I read somewhere that SM5100B takes 3A at full peaks.
In my opinion the power supply must be above 2 Amp. Try one with 2.5A or 3A.