Not running a thermostat most likely will help your engine run cooler, but you lose many benefits.
First of all, the thermostat is there to help the engine heat up to operating temperature as quickly as possible. This is essential for long engine life. Contrary to belief, engines need to run at a certain temperature, cooler isn't necessarily better. Of course running too hot isn't good either.
Secondly, the thermostat acts as a restriction, preventing coolant from flowing or cavitating back towards the block. Think of it as a sort of check valve.
That being said, the optimum setup for an engine is a thermostat that warms up the engine as quickly as possible, then allows the optimum amount of coolant to pass to keep the engine at that temp. The harder you drive, the lower temp thermostat you need, to help bleed off excess heat created from hard driving. These conditions vary depending on climate and driving, thus the reason Nissan offers different temp thermostats.
Removing the thermostat completely is a mistake IMHO.
A thermostat is absolutely necessary because it holds the temperature within a set range designed to produce the correct clearances between parts made of different metals. Aluminum expands much more that cast iron for a given temp change. Too cold and you have piston slop and uneven seal at the head. Too hot and you have not enough piston/cylinder clearance and a warped head. If you are having overheating problems, fix whatever is wrong and keep the recommended thermostat.
Maybe you guys can help me with this, when my Z is at operating temp I can feel the heat under the dash like if the heater is on but its not blowing. The guage reads good but the engine seems to be running hot if I can feel it to the point where I have to put the windows down. What do you sugjest?