Find a mechanic with a scanner that displays live data and see what the actual temperature is. You can also observe how hot the air is coming from the heater. If both are normal suspect the sending unit for the gauge although they normally cause very little trouble. A corroded terminal in the connector would be more suspect.
It's unlikely two thermostats would cause the same problem but look at the old one to see if there's a small bleed hole in the middle of it. That is to prevent gauge fluctuations during the first few minutes but in some applications where it isn't needed, that hole can allow the coolant to flow before it has a chance to warm up fully.