It's grammatical to start a sentence with a variable but the latter variant, "The variable Φ is treated in a special way", is less confusing in the following ways:
- The latter variant makes it clear that you're talking about the variable Φ and not about anything else, such as the sentence Φ or the function Φ.
- The latter variant makes it more explicit that it's a new sentence, i.e. a dot, a space and a capital letter is a clearer indication of a new sentence than only a dot and a space (this may be less of a problem with certain typesetting techniques, e.g. if your text is typeset with English spacing since it makes new sentences more explicit by adding more than inter-word spacing after each dot ending a sentence).
- The meaning of the latter variant is more self-contained and this makes the text easier to understand when only reading excerpts of it, e.g. if quoted.
Also, the latter variant is advised against by http://www.chicagomanualofstyle.org/CMS_FAQ/Numbers/Numbers26.html.
There is one thing that speaks for the former variant, "Φ is treated in a special way", and that is that it's less redundant given that you've explicitly stated that Φ is a variable so that it's obvious to the reader.
If you favor the former variant but want to avoid its deficiencies you might want to consider to incorporate it as a subordinate clause in an appropriate sentence, e.g. the sentence before it.
Think carefully whether or not the latter variant is redundant. If it's clearly redundant you might want to avoid it because being overly explicit can confuse or irritate the reader as much as not being explicit enough.