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The coolant that flows into the heater matrix inside (that provides the cabin with heat) is not heated by the EGR cooler. The EGR cooler is designed to use the coolant to cool down the hot exhaust gas before it hits the intake manifold. If you block the EGR valve, the largest effect you give to the motor is the removal of hot exhaust gas from the intake. There is a very minor change in coolant temp because when the EGR valve is open and hot exhaust is flowing (note that it doesn't flow all the time) there is a small rise in coolant temp - but it's not much, because the cooler is so small it doesn't really get a lot of a chance to heat the coolant up.

You could bypass the EGR cooler (if you're going to replace the EGR valve and unblock the EGR tube, this should be temporary only). You could also undo both of the coolant hoses from the firewall and try pumping water through it to see if there's a blockage, but don't use a lot of pressure in case the blockage decides to vent itself in other ways inside the cabin!