This logger has some analogue channels, but the data sheet I found was sparse on info. It didn't say what the input configuration or voltage scale was, only that the resolution is 1024 steps. This means you would have to play around to discover the actual value, by using a low current voltage source, and check the reading to see what voltage equalled counts. As the power supply is a 1.5V battery there are few clues, but the full scale might be 0 to +5V, or 0 to +10mV. Ask the manufacturer, but I suspect this is deliberate, so you use their accessories.
Armed with this information you then need an electronic circuit that converts the AC or DC current in the range of the heater to DC voltage in the range of the logger analogue input. If you only have to know the heater is working, and the current it draws is continuous or thermostat switched, the logger averaging will give some sort of result proportional to the time it is switched on - heating. The NRG heaters are "self regulating".
Assuming you are using the NRG heated sensor, the heater power supply seems to be 24V AC @ 250W, and that can supply 2 sensors. That means the AC current is 5.2A for each sensor.
The first link below has several devices that would suit. Ask a sales person for help in measuring 5A AC as a DC voltage at a data logger analogue input (as these all have over-range capability 5A is fine).
A current to voltage transformer could transform the AC current to AC voltage proportional to the current. The transformer must have a load resistor (burden resistor) to suit the transformer. The output is about 10V AC for rated current, and importantly it is isolated. In the link below see the CR3100 series.
The logger only operates with DC inputs. It very likely needs a low source impedance, usually taken as <1K in parallel with 0.1uF. I suspect the inputs are directly connected to a microprocessor chip, and need some sort of protective circuit. Partly why they have been left unspecified so you contact the company.
A current transformer needs a small bridge rectifier and filter, and such a rectifier on the voltage winding will need a few volts to operate properly. The circuit is a burden resistor across the transformer secondary, with a bridge rectifier. Connect the plus output to a series R of 47K and a shunt C of 2.2uF. This provides a DC voltage something like the AC voltage, so 0-10V, and proportional to AC current. You will need a voltage divider (the tap from 2 resistors in series across the capacitor) to get this to the logger analogue input voltage range, but also an amplifier to convert to a low impedance source for the logger. Look up a non-inverting op-amp (gain of 1) which is quite simple, but will need a small dual power supply, providing something like +12VDC, 0VDC, -12V DC @ a few mA..
Another idea is to use the CR9521 current sensor (0-5V DC out, proportional to AC current). It must have a burden something like 1 meg-ohm, and will need a voltage divider (~1 Meg-ohm total) and non inverting op-amp between the output and the logger analogue input.
Yet another idea is an AC current operated switch. The second link shows one way to do this, but there are many kinds of such switches out there. It will provide a relay or NPN transistor switch output that can be used to switch a voltage on the analogue input that is recorded as an off and on status signal. Thus current is ok or not ok.
Finally, you could consider a temperature sensor (as the NRG company has this) near the heater. It may be necessary to have a second temperature sensor for air temperature, and take the difference later in software. This has an advantage in that you are also getting a data set that could be useful later. I would also contact NRG for advice. They may have an off the shelf solution.
You may need some help with any of these ideas, and one thing to do is make sure they work properly with a multimeter (DMM) first, before anything is connected to the logger, as the logger analogue inputs are probably quite fragile.