Heating Vitara Hybrid Allgrip

I bought myself a Suzuki Vitara Allgrip Mild Hybrid and was at first quite happy that it actually drives a lot purely electric. However, I had to find that in pure electric mode the heating gets out. According to dealers, no electric heat pump is installed in the driveway. So the car in e-mode only pumps cold air into the vehicle interior because the water pump driven by the petrol engine does not run. My question, is that also so with you? Is it true, what d he tells dealers – freezing for climate and purse?