I'd say, take the card out you have for physx, completley pointless, is probably throwing out a lot of extra heat and blocking cooling, unless you don't have it in anymore.
Heat vs noise is how most cards run, 81c isn't hot, the card shouldn't crash up to 100C+, its not cool either though.
Some manufacturers go for higher temps and the lowest noise output possible, others go for higher noise and lower temps, some have high temps and high noise, because they're retarded.
First suggestion would be to increase the fan speed, even above acceptable levels just to see if the second screen cutting out continues to happen or not.
Basically, it shouldn't, and normally 81c full load shouldn't be enough to cause a card to simply stop running the second screen. I'd think it would be more likely a fault with the card.
Depends what version you got, first try afterburner from MSI install, see if you can change the fan speed with it, I'd imagine you can if its a default 460gtx or a MSI one obviously. If not try whatever software the card came with, or from the manufacturer you bought from.
If for some reason theres no fan control, try downclocking the card for now and dropping voltage a little if at all possible see if that causes a reduction in temps and the second screen to not shut off.
My first thought is, faulty rather than better cooling required, though I'd also google, maybe its a driver issue other people have, I don't think its particularly common if it is a driver problem as I've not seen it mentioned.