I think my car does not have a thermostat, it vibrates in neutro or Park, why?

What is your question?

also the temperature is always very low and the fuel consumption is very high not normal for this vehicule. I want to change the thermostat as soon as possible but am worried that has been like this far too long and now may be vibrating because some other failure that this could trigger. i just buy the car and want it to stop vibrating. thanks for any recommendation of what could be.