I think you're underestimating what the car can take! It'll be fine as long as you don't go nuts, or run it continuously all day.
My advice would be to definitely book in with an instructor, perhaps a couple of 20min sessions, one early in the morning if you can. That'll help you get comfortable on track, learn where to brake/turn-in etc.
In terms of taking it easy on the car, when you go out, build up over a lap at least to get tyres and brakes warm, do a few laps, then make sure you do a cool down half/full lap to get some airflow cooling everything back down. When you bring the car back in, do not use the handbrake - just put it in gear and turn the engine off. About 15-20min on track is about the max I'd want to do before coming back in. You can take a break as long as you like.
I just remembered something else. Years and years ago, I did an all day driving training course with a company called Ride Drive. I went out in the morning with an ex-police instructor, who showed me the police advanced driving methods on some nice B roads (lots of driving on the wrong side of the road at speed), and then we went to bruntingthorpe for a couple of hours - did some handling sruff, then laps around the track. We would have then done more road driving in the afternoon if my clutch housing in my S4 hadn't disintegrated down the back straight on the final lap!
That was a shame, but the car was on 80k on the original clutch, so it was due to go. Aside from that, it was a good day and included a bit of track time. I got a certificate at the end of it that gave me a discount at Adrian Flux.
They have instructors around the country, might be worth giving them a call.
http://www.ridedrive.co.uk/performance-driving-menu.htm