Yamaha TZR 50 2 stroke - Overheating and high tickover

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So I've just turned 16 and got a 2009 yamaha tzr50 2 stroke. It's de-restricted and manages 50mph at the moment. It's got an arrow pipe on it, it been upjetted and tweaked to run a bit richer and also being geared for good acceleration and speed.
Recently when I've been at 9,000 revs for about a minute (redlines at 10,000 and maxes out at 12,000) the engine temperature light comes on and stays on for a while, then eventually goes out. Bear in mind it doesn't have a fan. The bike is definitely not running lean. It has enough coolant in it, I've ordered a new thermostat just in case it's that (I doubt it though). My verdict is possibly blocked pumps or rad but just wondering if anyone's got any other ideas?

Secondly, when the engine temp light comes on, when I come to a stop the tickover will stick between 2,500 and 3,500 revs for a while until the light goes off, then it will gradually go down and settle at 1,700 which is my idle setting, any ideas about this too?

Many thanks
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Yamaha TZR50

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Liquid cooled then? What is the state of the coolant and level? Is the radiator clean and debris free?

The thermostat could also be stuck/sticky if it has one. On the old TZR250, this was at the top of the cylinder head, with the water hose attached to it.

If it's only at high revs, I doubt the pump is at fault, unless the seal has gone. What does the gearbox oil look like, oily or milky? any bubbles in it?

Pull the plug and post a picture of it. It may still be running lean, even with the jetting being upped a bit.
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TZR250 2MA road, TZR250 1KT road, TZR250 2MA race, TDR250, YZF-750R Boost colours.
Jaguar S Type 3.0 V6 Sport R, VW Transporter T5 GP LWB Shuttle 140ps DSG.