This could as already stated be a sign of a hardware issue in the PS3 itself, However don't overlook the possibility of it being a television problem. Try hooking up to another tv, and if that does not fix the problem there may even be something up with the AV or HDMI cable you are using. if swapping out these things does not help and you are still under a warranty I would recommend downloading all your save files to flash drives and return the ps3 for a new one.
as for the heat problem try to keep your PS3 in a well ventilated area. if this does not help it is more than likely either due to some sort of heat sensor problem or something to do with the fans.
Original Answer
You're not effecting the tire choice of the car, just the wheel rim.
I've tried many different wheel and surface combinations in a number of vehicles and haven't noticed any difference in terms of the cars handling.
Someone may be able to disprove me with numbers or something more empirical, as my evidence is purely anecdotal, but aside from the bulletproof tires, I believe all of the wheel mods are purely cosmetic.
EDIT: I've revisited my answer below.
Updated Answer
Some people with more time and patience than myself have taken the time to run a few tests and document everything.
Like this reddit thread where the poster records his times using the same vehicle with various upgrades on the same track surface, including stock car with each wheel type. This particular set of numbers reflects an extremely negligible difference between the wheel types.
There is also a YouTube video showing a slight difference in traction for the Off Road tires.
There is also this reddit thread where the poster comes to the conclusion that the difference is somewhat negligible.
So, there is a lot of anecdotal evidence and some video, but I don't think anyone has found any confirmation in the code that wheel type has any modifier effects for a vehicle.
In summation, your mileage may vary.
Best Answer
On PC, if you activate the weapon wheel (Q) you can hover over the weapon type you want. If you want (and own) another weapon of the same type, scrolling the mouse wheel will allow you to change into that other weapon.
For example, if you own both the AP Pistol and the Silenced Pistol, you over the top center portion and use the mouse wheel to swap between AP and Silenced Pistol.
Do note that the Weapon Wheel will also show you how many weapons of the type you're hovering you own.