Renogy MPPT mounted inside?

Proximity to battery and remote temp sensing are 2 different things.

You want controller to be (reasonably) close to battery to avoid too much energy loss in the wire at 30-40A, and also to prevent misread battery voltage sensing by controller. Use Voltage drop calculator to calculate the required wire gauge. Enter 2% loss and ONE-way cable length to battery.

A good controller will have remote voltage sensing - don't know if your Renogy does. If it does, then you can go up to 3% losses if you have to. Daily difference in AH harvest between 1% and 3% losses will be mere few AH on a sunny day, this is nothing. On cloudy days this difference will be below detectable level.

Most MPPT controllers 30A and higher have a remote temp sensor - a necessary thing if temperature in battery closet and temperature at controller location differ by more than 5F. If it does differ, and if you have a remote temp sensor, it should be attached to the battery.

Again, a good controller will have a (optional) remote display. Apparently yours don't have it, or you chose not to buy, otherwise you wouldn't have started this thread. No big deal, as long as you can see the main display.

My 30 amp MPPT Rogue always feels ambient temp to me when I touch it in various modes. It is in a pass through cargo bay.

How much heat it radiates will be affected by your choice of wire size, and the number of amps they're carrying.

Just inside the door is the best place for a flush mount LED.
Can be seen inside or outside.

Unless it has a remote temperature probe it needs to be as close to the batteries as physically possible. Temperature compensation is very important for correct battery charging.

Mount it anywhere inside. Away from a traffic area would be best. Solar controllers dissipate very little heat. The large heatsink is to accommodate the highest possible heat dissipation from the components within the controller case and is engineered for higher ambient temperatures than is typical. In use, it will be barely warm.

MPPT 30-40A and bigger all have a huge (and ugly) heat sink. The whole gizmo was rather unsightly (different brand, not Renogy), and I hesitated a little before mounting it inside. Especially since the most convenient location - closest to batteries - was in the bedroom. I didn't want it in the cargo bay as I didn't purchase a remote display with control buttons - it's all on the front panel - and it would be difficult to see the on-board display in cargo bay. Besides, my cargo bay is not too big and I have other items to store there. Besides, there is more dust, humidity and salt air in cargo bay.

I don't notice much heat at 20A - and it rarely shoots higher because my battery bank is big, compared to my energy needs, so in the morning it starts from 80-85% Full and by the time there is enough sun to generate 30-40A, my batteries are in Float and draw mere few amps.

It makes soft clicking sound when switching between the modes (not very often), and the sight of a big white brick on the bedroom wall is something to get used to. Thanks God the display is gray LCD (backlight when needed), not a bright red like Trimetric or some controllers brands. 1/4" wall panel can be a challenge to mound 5-6 pound brick.

My manual recommends 6" clearance above and below. Check your manual and go ahead.

Its a SOLAR controller
Not an electric heater
14v 40 amps 560 watts max pass thru
If it had all OF that in heat nothing would be going to the batteries
Mounting on the wall is not going to affect the way your A/C works
But that big wire is not going to be pretty