Heat blows warm air

feel the temperature at the heater hoses in and out of the core at the fire wall, are they both the same temperature?both hot? if not you may have a blocked heater core and if both are hot to touch, the blend door may be stuck and not allowing hot air to flow into the cabin, have these checked first.

Done that. could it be a weak water pump that make it do that?

Just to add this one the water pump is not going to be weak they always work. If you have one warm heater hose and one heater hose going into the heater core at the firewall you have a restricted heater core like mhpautos mentioned earlier.