You're right. The positive or negative sign in that expression is just a bookkeeping convention and doesn't really have any further consequences. In some sense, it's a one-dimensional problem (the "heat dimension"). An EM analog might be nodal current analysis. For the purposes of analyzing nodal currents, it doesn't actually matter if you say that the sum of all the currents is zero, or if you say that the sum of currents flowing in, minus the sum of currents flowing out, is zero (and call all of the currents positive). In either case, you're preserving the information about whether something is going in or going out, just with a different system of bookkeeping -- are the negative signs attached to each current individually, or a group of currents that you identify and sum?

Once you start involving multiple spatial dimensions, as is common in EM problems, of course your choice of sign convention has more implications downstream.