not necessarily. If the engine doesn't overheat, then its not an issue. Thermostat will open up when water is hot enough and if the truck always goes to the same temp and stays there, regardless of outside load or temp, then you are ok.
If it gets hot out and the truck does overheat, then the radiator might not be able to remove enough heat. The only thing that would help at that point is to increase cooling capacity by either a helper fan, or, more radiator. There maybe some additives like I used in my race bike that can help too (like water wetter).
The thermostats all let through about the same amount of water. Its just when they are going to open up. An old trick is to remove the thermostat, but then the truck will run cold, and take longer to warm up.
What do the plugs look like?