How to Use a Johnson Digital Temperature Controller with a Fermwrap - General Questions

This is my first temperature controller and first use of a Fermwrap.

I understand that the Johnson A419 Temperature Controller can only do hot or cold at one time. Which mode does it default to when you buy it?

I plugged in the Fermwrap into the controller and set the controller's set point to 80F. The Controller read 66F, but the Fermwrap did not warm up. Not sure whether or not the default mode was cold, I set the set point to 50*F and a green light switched on. I assume this means that the Fermwrap is about to warm up. I flipped the jumpers to set the controller to hot mode.

I set the controller's set point to 80*F and the differential to 1.

I laid the Fermwrap on the ground and put the johnson probe directly on it, and the probe quickly warmed to ~74*F.

I then taped the Fermwrap onto a carboy full of water. My Raspberry Pi with its waterproof DS18B20 temperature probe is telling me the water is 65.18*F. The Johnson probe that I taped to the carboy with styrafoam is at 68*f.

The water in the carboy is not heating up -- How hot can the Fermawrap get? Or more appropriately, given an ambient temperature, let's say 40*F, can the Fermwrap pull the carboy up to 60-70*F? I've read about people using a freezer with Fermwraps wrapped around a carboy to support ale temperatures, so I would think this would be OK.

I'll update this question, but the carboy is not moving up in temperature. The Fermwrap barely goes around 1/2 of the circumference of the carboy.

I'm wondering if it will just take a while to heat that much water and/or if the Fermwrap is simply ineffectual. The temperature is supposed to drop to 45*F tonight. Can I expect the Fermwrap to counter the drop in temperature quickly enough?

Are there any tricks I should be doing? I thought about wrapping the carboy in some kind of insulating material, but the piece of paper that came with the fermwrap suggested that this would be inappropriate.

Edit - 17:50 PST the temperature of the water has increased from 65.18 to 65.3.

Edit - 18:10 PST increased to 65.4116*F

Edit - 18:50 PST increased to 65.6366*F. The Johnson probe on the outside of the carboy says 72*F. I thought it would have been in line with the temperature of the water in the carboy.

Edit - 23:10 PST increased to 68.45*F. Johnson probe reads a whopping 76*F. This doesn't look good.

Edit - 01:00 PST increased to 70.025

Edit - 10:00 PST the following day increased to 72.95. The Johnson probe reads 72. This looks better.