Too complicated and I think by the time the thermo switch adjusted itself the Pump reservoir would be empty. No offense.
I wouldn't agree.. it's by no means overly complicated..
in fact it's practically as simple as finding the thermostat that triggers the warning light in your cooling system.
(not the one that switches the radiator fan)
and tap into it...
as soon as the warning light goes on, the pump would start pumping to help cool down.
You can add another thermostat of course if you fear to mess with the engine electronics even the smallest bit.
Or you don't have a trigger switch since that's taken care of by the computer based on a temp sensor.
that'd mean adding a few dollars for a thermo switch (IDK 10 maybe)
this time a cooling fan switch would be indeed the one you'd want
(triggers a bit faster but we're furthher from the heat so that'd do)
and a way to mount it touching the radiator (some sheet metal you have)
based on the temp switch you got (most trigger at ~110°C [roughly 200F])
and the fact that they're threaded you can leave a small airgap between the switch and the radiator case to adjust the coolant temp it triggers
And of course you can still -in parallel- install a push button to your dashboard

(which in fact is more difficult.... fiddling another set of cables through that nasty throughhole under the dashbaord)
'sid
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EDIT]
Oh wow.. thermo switches are expensive nowadays... odd..
anyways, for less than 15 bucks you can have one for sure on ebay...