I've been thinking about this and the theoretical answer is the <

Ideal Gas Law>

However I can see that defining all the terms in your practical problem would be difficult.

Would it be possible to directly measure the temperature of the gas entering the tire?

Given this you can work out the energy required to raise the temperature the required amount.

The <

molar heat capacity> of Nitrogen is 29.124 J/(mol·K)

which means that it requires 29.124 <

Joule> to raise 1 mole of Nitrogen by one Kelvin

One <

Kelvin> is essentially the same as 1 Celsius (or 1 degree centigrade).

(Kelvin, Celsius and centigrade differ only in where they are defined to be zero,

0 K is equivalent to −273.15 °C {−459.67 °F})

A <

mole> is a defined (very big) number of nitrogen molecules (602,214,076,000,000,000,000,000 molecules)

one mole of nitrogen has a mass of 14 grams.

at 1 Bar (14.5 psi) 1 liter of nitrogen has a mass of 1.25 g.

1 watt is 1 joule per second.

So from your flow rate you should be able to work out, theoretically, how many watts you will need to raise the temperature by the required amount.

However, in practice you will have inefficiencies, so you will need more than this.

In the end you may find that trial and error will be your best bet!

Note that where I have <> there are links to relevant Wikipedia pages.