Coolant system flushin 96 A4

Need to replace the T-stat on my 96 1.8 (ADR) A4 so I thought it would be worth flushing the cooling system while I'm at it. What's the best way to
flush out the heater matrix? If I start the car and crank up the heat & then turn it off will the valve stay open so I can just stick a hose onto the inlet stub? Its got climate control on it (Red digital display with buttons to alter all the various heater/aircon settings).
The thing has Green (G11?) Antifreeze in it at the moment & I got G12+ from the dealer which is all they sell now and can (alledgedly) safely be mixed with G11 - but I think I'd rather just get all the old coolant out altogether.
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