Sounds like the extension lead is probably not up to that load continuously.
Firstly, make sure that the extension lead is fully unwound and rated for the full 13 Amps. Many are only rated at 6 or 10 amps. You really need 1.5mm 3 core flex at the minimum to handle that current, so see if the cable has any markings on. It may well be only 1 mm.
If that seems well, make sure the plugs are wired neatly, with the cables securely clamped into the terminals and no stray strands of wire broken off or outside the terminal. Make sure the pins are clean too. A rub with steel wool or wet & dry wouldn't go amiss. You're looking to reduce the resistance at each of the connections. If either of the plugs are cheap and nasty replace with a quality make such as MK.
To be honest, for a 13A plug to carry the full 13A load continuously (which is what is being asked of it for a 3kW heater) is quite unusual. Other high power appliances such as kettles and heaters are generally only used intermittently and these days are normally around the 2-2.2 kW range. I think you can expect a little heat in the plugs, but obviously you need to take a view on whether it's getting so hot that it'll cause a problem.
When you look at appliances that are likely to draw 3kW for hours on end (e.g. Immersion heaters) they are on their own spur and hard wires into a spur box, for good reason.
The best way to do it would probably be to run a generously rated RCD protected circuit in SWA into the garden and hard wire it using a suitable waterproof fitting, but that would need to be carried out under Part P.
Failing that, make yourself up a better extension lead using 1.5 or even 2.5mm flex with quality fittings at each end and only make it as long as it needs to be.