Your voltage should be the same as if you are using 50 amps, ie about 120. It is only the amount of current that you can use that is reduced when you use a 30 amp service.
Here is the way it goes:
50 amp service means you get 50 amps of 120 volts on each leg of your Monty. So, you are actually getting 100 amps, an amount you will probably never exceed.
30 amp service means you get 30 amps of 120 volts spread over each leg of your Monty. So, you are only getting 30 amps. This is because a 30 amp adapter takes the one supply of 30 amps and combines it so that it can flow to each leg. If you use the microwave and the hot water heater and the air conditioner, you will probably exceed 30 amps. With 50 amp service you would have to exceed 50 amps on each leg of service before you would trip a breaker.
Now, to your original problem. Your thermostat does not operate on A/C current - it operates on 12 volts DC, so your being plugged into 30 amps has nothing to do with the problem you are inquiring about.
Hopefully, someone can help you with your thermostat. I just wanted to give you a better understanding of your shore power hook up.
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