I'd definitely report this to the service manager of your local Mazda dealership. The driving conditions you describe typically wouldn't result in an engine overheating. I personally wouldn't drive a car that gets into the max H line even though it may not appear be overheating, just to be on the safe side. Most likely it's probably a defective temperature sensor in the engine block.
One test may be to monitor the gauge and when it starts rising to about
3/4, pull off the road and turn off the engine and take the key out of the ignition so all systems are off. Insert the key and turn it until all the lights and gauges go to their normal positions. If the gauge goes to half, it's your temp sensor. If not, it could still be the temp sensor giving you a false reading. It's best to take the car back to Mazda and have them thoroughly check the cooling system. My hunch is that you have a faulty gauge or temp sensor.Hope this helps.