At 2 kW, a plug will likely get mildly warm. It shouldn't get hot.
the fuse blew ten minutes after posting... put another in (5amp as opposed to the 13amp that blew), that lasted half an hour and blew. I guess the heater is fooked
I'm not surprised. Your heater's drawing about 8-9 Amps. As a rule of thumb, a fuse will only blow at around 1.5 times its rating, and even then, it'll likely take at least 30 minutes or more to heat up sufficiently before it ruptures. Your heater's probably not drawing a huge current.
A 13 A fuse can get quite hot, even in normal use. That can cause the contact between it and the fuse holder to oxidise, increasing its resistance so making things hotter. Try going over the fuse metal end caps and the fuse holder contacts with a bit of sand paper and seeing if the plug still gets hot afterwards. (Remember to unplug it first before!)