If I am picturing what you are saying the same way that you are, I think that might work. I am picturing you basically splicing the hot water line directly into the cold water line somewhere before the outside spigot, and then having a ball valve on the hot water line right before that splice to adjust the flow of hot water going into the cold water pipe. Then you shut off that ball valve to mechanically shut off the connection between the hot and cold water lines when you are not filling the aquarium. Then you hook the aquarium hose up to the existing spigot, turn the spigot on, and get aquarium temp water at the aquarium through the now cold water only spigot when doing the water change. Then if you flip the ball valve to the off position when finished filling the tank, the spigot once again becomes only a cold water spigot that still has the full flow capacity.
That could work, but I have not tried it exactly like that before. Theoretically, if you have both the hot and cold water pipes directly spliced together with no restrictions, then you would have a perfect 50-50 mix of hot and cold water coming out the pipe with the mixed water after the splice. In practice you only need around 1/3 of the water to be hot in order to raise your cold water up to aquarium temperature, so having the adjustment valve on the hot water line to restrict its' flow some to achieve this ratio would work. You might consider doing the same thing except combine the two approaches to make it more user friendly. Just tap the hot water into the cold line like you were saying, but have a screw type of valve like a regular spigot on the hot water in addition to the ball valve. Just have one right after the other. I am just nervous about the ball valve's ability to finely adjust the flow of hot water, because they are really made more for an on-off application only. A screw type of valve would allow you much more control over mixing. Then you could do the same thing with setting the screw spigot initially and leaving it alone and only using the ball valve right after it to turn the hot on and off. That way the temp remains set between water changes so there wouldn't be any adjustment necessary each time.
This setup would pretty much be exactly in the middle of what I initially gave you in the drawing and what I think you are saying in your reply, and it would give you the best chance of making the setup work well enough to be an asset rather than a possible hassle.
One thing that might be a problem, is that this setup might be much more sensitive to any line pressure changes while it is operating. When you open the existing spigot at the end of the line right at the tank, depending on how far you open it that will change the line pressure between your mixing setup and the spigot you are adjusting. For instance, if you just open the hot water ball valve to connect the hot and cold water mechanically, then nothing actually happens in the lines until you open the other spigot that you have at the end of the line by the tank. Only then is a pressure differential created, and the hot and cold water begin to mix and be pulled towards the aquarium. The more you open the existing spigot at the tank, the greater the pressure differential becomes between the hot/cold water and your mixed water. You will probably find that the water temp changes not only from how you set up the system initially, but also from how much total flow you are pulling through the system as a whole. That could make it more of a hassle for trying to make this setup work well over time without a little fine tuning every time you use it. I don't think it would be that big of a deal, but it would be an issue that would make things a little less consistent and repeatable each time you do water changes. That would essentially be creating with two valves exactly the situation one encounters with their single handled shower valves. On the shower, if you pull out the handle to turn on the water to a certain pressure and then rotate it left and right you can fine tune the temp, but if after you reach the right temp you decide that you need more water flow and pull out the handle a little more it is very rare in my experience that the temp doesn't change a little and need to then be adjusted again. Changing the flow with the existing spigot at the tank would be the equivalent of moving the shower handle in and out. I hope that makes sense.
This setup could work, and to be honest I think it is worth a try, because it uses the same parts (and less of them) that you would need for a different setup like the one I initially drew, and it would be very easy to hook up, so all you would be out is a little time if it didn't work well.
If you do find that your temp changes due to both valves, maybe just draw a black line on the top of the spigot (at the tank) and for instance always turn that valve on two and a half turns so that way your flow rate is almost exactly the same every time you fill the tank. Then you could probably end up with a more “set it and forget” it type of water changing system to where all you do each time is flip the hot water ball valve, and turn the main aquarium spigot the specified amount of turns to set the flow rate, and then just do the opposite to turn everything back off.
Good luck, Jeremy