Is it a desktop computer, or a notebook or netbook computer ?
"using a wired mouse "
Which type ?
PS/2, USB, or Serial ?
Does it have a ball inside of it ?
Is it a touchpad mouse ?
(They're a lot more sensitive to temperature.)
"It only happens to me in the heat of the afternoon when the sun is shining on my PC."
That's not likely to make any difference, unless the computer is getting VERY hot when it's in the sun, or unless it's a touchpad mouse.
How high does the air temp get where the computer is when it's in the sun ?
What color is the mouse ?
What color is the computer case ?
(If it's black or dark colored it will get a lot hotter in the sun than when it is white or light colored.)
If it's a touchpad mouse, keep it shaded.
For that matter, whatever type of mouse it is, try keeping it shaded.
"have been using malwarebytes and security essentials since day one."
I have NEVER come across ANY mention of malware causing the mouse cursor to move on it's own.
That behavior in my experence and from what I've read has always been caused by a hardware problem - there is a problem with one or more wires inside the cord, or the mouse is actually moving slightly when you don't have your hand on it (e.g. due to vibration), or it could be caused by too much heat in some circumstances.
I DO know that some touchpad surfaces are much less responsive when they're too cool, so it makes sense that they may be too responsive when they're too hot.
If the computer's CPU is getting way too hot for whatever reason, that can certainly cause odd hardware behavior.
The current CPU temp reading is shown in the mboard's bios Setup.
If this is a desktop computer, the most frequent reason for the CPU getting too hot is there is too much accumulated mung - dust, lint, etc.- on the CPU fan and CPU heat sink.
If the cpu fan/heatsink has mung (dust, lint, etc.) on it, clean it off, but DO NOT use a vacuum cleaner to do that (they produce a tremendous amount of static electricity when running, and anything connected to them can discharge that to your components) - use canned air, or an air nozzle if you have access to an air compressor, or an artist's brush that can be used in small spaces, etc. It may be difficult to clean the top of the heatsink under the cpu fan - the most likely place to have mung on it - and the bottom side of the cpu fan blades unless you remove the fan. If you have a case fan, clean that too if it needs it.
Also check for mung on the video card fan and heatsink if it has that, and the power supply's openings / fan.
If you have a notebook or netbook computer, the cpu may get too hot if
- you are obstructing air getting into and out of the openings in the base of the case
E.g. you're not using it on something flat and relatively rigid.
- there is too much accumulated "mung" - dust, lint, etc.- inside the air passages inside the laptop - sometimes you can see that from the outside at an opening where you see fins by shining alight into the opening.
- the fan inside the case is spinning too slowly because of failing fan bearings, or it isn't spinning at all (it should come on occasionally)
If the fan makes rattling or rumbling or screeching noises, most likely to be heard when the computer is started after it has cooled to room temp, replace the fan as soon as you can - it will probably eventually stop spinning if you don't..