Heater only gets warm once car starts moving?

Faulty thermostat.

It's not closing properly, which lets too much coolant flow to the radiator and that keeps the engine cold when it's idling. When you are actually driving more heat is produced and the engine is able to warm up.

BTW, warming up an engine like doesn't do it any favours, and just wastes fuel. Just drive sensibly for a couple of minutes and it will warm up fine, with less engine wear.

Depending on what vehicle it is, I would say that a remote start is really only good for defrosting your windshield which in turn heats up the whole vehicle decently. As a michigander with a 2015 Silverado, 2 cycles and my truck is decently warm but not as warm as what I'd like it to be.

This is pretty normal for a vehicle actually. It's main function is to ensure efficient running; your comfort comes behind this. For this reason, it maintains the proper engine temperature by bypassing the small radiator that is used to heat the passenger compartment. It won't let much warm coolant through to the heater until it's up to optimum operating temp. Nothing to worry about, this is how it was designed.

Total waste of time and gas to run the truck for 20 minutes. Move off as soon as the windshield has cleared.

Just start driving it.

No use letting it sit and waste fuel and wear the engine for 20 minutes while running cold oil and low oil pressure.

That is kind of normal, depending on the idle speed, the outside temperature, and your truck's thermostat. As you drive the truck and the engine has to work harder, it'll heat up faster.

Your cooling system sounds low on coolant. Not your reservoir.