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First off, to determine GHA Aries you're going to need a calendar.  You don't mention having one but you can't really go between GHA Sun and GHA Aries without passing through UT date and time along the way.

The relationship between GHA Aries and UT has a fixed definition that increases.  The rate is almost entirely linear and treated as an increase in GHA Aries of 2.46' per hour UT by the Nautical Almanac.  Historically this difference has been referred to as the "right ascension of the mean sun" and some modern texts still refer to it by the letter R.

Separate from this is the relationship between UT and GHA Sun, known as the "equation of time."  Throughout the year GHA Sun varies with respect to a given UT by as much as 4°.  It can be approximated as the sum of two sine waves:

• period of 1/2 year, amplitude of 10 minutes (2.5°), zero points at equinoxes and solstices
• period of 1 year, amplitude of 7.5 minutes (1.875°), zero points at perihelion and aphelion

Both factors push the sun west of UT in mid December and east in mid January.

You could figure out the first part by knowing the name and amount of the sun's declination and whether it's increasing or decreasing, but the latter is based on the sun's distance.  At the scale of 0.1' the sun's SD might give you a vague clue, but that too wasn't listed as one of your known values.