Question: I increased the temperature of the water heater and now every once in a while the T&P hose/pipe will drip. Was I supposed to adjust something there as well?  

I ensured that the temperature on both panels was the same.  

[![enter image description here](https://i.stack.imgur.com/WXYqBm.png)](https://i.stack.imgur.com/nMFUf.jpg)
[![enter image description here](https://i.stack.imgur.com/nMFUfm.jpg)](https://i.stack.imgur.com/WXYqB.png)

Answer: 
Water expands as it's heated. If there is something that acts as a check valve (most commonly a pressure reducing valve, (PRV) rather than a check valve as such, for a municipal supply) the expansion translates to a significant pressure rise unless there's something else to accept that extra volume without such a severe pressure rise. So, the pressure gets too high and your pressure relief valve opens.

The solution is a trapped air bubble, usually in the form of a small "bladder or diaphragm" type expansion tank. That has an air bubble on one side of a rubber membrane, and water on the other. The pressure rises, but not as severely because the air can be compressed, while water is effectively incompressible. Unless they have unfortunately positioned check valves, folks on well systems have the same function served by the larger pressure tank that serves the well pump, so they don't require one specifically for the water heater.

If there is no expansion tank, or the rubber separating the air from the water has failed, an expansion tank typically needs to be added or replaced.

It is generally not possible to set the temperature so high that the temperature part of the relief valve is actuated, unless the thermostats are defective, so it's almost always due to overpressure. If you have a pressure gauge you could observe its behavior, but many municipal supply water systems lack even a single pressure gauge. Typically you see the pressure rise significantly when a lot of hot water is used, and replaced by cold water in the heater, and then little or no water is used while that water heats up and expands.
You need to install a potable water expansion tank. The size of the tank you need will depend on the size of your hot water tank and the supply pressure. You can measure the supply pressure by picking up a gauge like this: <https://www.homedepot.com/p/Watts-3-4-in-Plastic-Water-Pressure-Test-Gauge-DP-IWTG/100175467> and attaching it to an outside hose bib or the cold water supply connection for a clothes washing machine. Attach the gauge and leave it overnight. This will tell you how high the pressure might reach when the local water supply is at its lowest usage.

Then use this PDF <https://www.watts.com/dfsmedia/0533dbba17714b1ab581ab07a4cbb521/20441-source/es-plt-pdf> to size the expansion tank appropriately. My guess is that PLT-5 is sufficient, but again that will depend on whether or not you have unusually high supply pressure.

Once you know the supply pressure, you will need to charge the expansion tank's air bladder to the same or slightly higher pressure using a pump -- a simple tire pump will do -- even a pump at a gas station if you don't have a pump yourself. Just make sure not to over or under inflate the air bladder or it will be ineffective. So if your street supply pressure is 50psi, inflate the expansion tank's air bladder to between 50 and 55psi.

In the same PDF, if you scroll down, you'll see an illustration of how to install the tank. You place it inline the cold water side entering your hot water tank.

With the PEX pipe you have in your attached photo, adding the tank inline should be relatively simple but you will need tools that you might not already have, like a PEX crimper and cutter.

Last thing to know-- make sure the tank is supported. So build a little shelf and strap the tank down with some steel banding.