The pre-departure climate control activation will not change your climate control settings to the ones that you need to warm the car. You must set the climate control, with the car switched on, to the settings that you would imagine needing if you jumped in and switched on the car and climate control a few minutes before departing. For whatever reason, I find that the "Max Defrost" setting seems to deliver the earliest heat of all settings I've tried from a cold start. The manual and online instructions seem to indicate that you must at least leave the climate control on the "auto"matic setting with a sufficiently high temperature selected (72F is their recommendation, I believe) that heat would be requested by the system.
I suspect that the heating system draws more current than your level 1 EVSE supplies, so you lose some energy from the battery during the warming cycle despite being plugged in. I have not had enough experience yet with our vehicle plugged into the level 2 EVSE to have an opinion about losing battery energy during such an operation, although I have monitored a Chargepoint session and noticed that the power draw grows during the warming. A 6.6kW-capable connection was drawing about 3kW while warming - clearly something that your level 1 EVSE won't muster. I think that leaving the system on Max Defrost before you switch it off and await your next departure will solve your immediate issue with the blowing only of cold air, and that a 240v EVSE capable of 3kW will alleviate any loss of stored battery energy while warming before departure.
