Sv650 2003 running problem - cuts out.

Hi all, I'm looking at buying my other halfs dads sv650, he's willing to let it go cheap to me however it has an issue, the engine cuts out when you shut off the throttle after accelerating, the bike seems to be running slightly rough also, the tenpreture readout on the clocks reads from 40 to 90 despite being wrm and also the battery is 5-6 years old, could the battery alone be causing these running issues? Bike is an 03 with 16k on clock
Cheers in advance for the responses

Battery could certainly cause all these issues. That would be my first port of call. Can you borrow one to test?

It starts on the battery? That means the battery is capable of being charged and delivering enough of that charge to everything that needs power to start the thing up. 5-6 years is likely near the end of it's useful life, but if it starts the bike, it's still OK, and if it's being charged so it starts the bike for the next ride, the charging system is working too.
Maybe the thermostat is stuck open?
Has it been sitting? Does it idle OK? Does it have fresh fuel?

Hi all, thanks for the responses, had the battery out tonight and swapped it for a brand spanker, bike runs better and cuts out less, however when back from test ride we left it on tickover and fettled with the wires that lead to the temp sensor, when moving them they caused the bike to cut out, we repeated this a few times until we were satisfied it was no coincidence, when ignition on we looked at the temp reading while moving the wires and this caused the temp sensor to jump from 50 - 70 and so on, could the wiring/plug really be the culprit? And in response to your question yes it has been sat for a while will get a fresh tank of fuel and some injector cleaner ran through on Friday
The issue is not when the bike is in gear and running back down the revs it's when it's moving and the clutch is engaged then it cuts out intermittently
Cheers again for the responses