Hello and welcome to Just Answer.
The short answer is no it should not.
Slow to get hot usually indicates that the thermostat is stuck open or missing altogether. Fluctuating wildly usually indicates problems with the temperature sender. It could be that the temperature is actually ok but the sensor isn't reading correctly.
It would be a good idea to take it to the mechanic and get it checked out in case there is something further wrong.
Check the coolant level and get it booked for a look at. If it is a sensor it's a simple job to replace.
If it is losing coolant then get it fixed pronto.