Certain example embodiments of this invention relate to edge sealing techniques for vacuum insulating glass (VIG) units. More particularly, certain example embodiments relate to techniques for providing localized heating to edge seals of units, and/or unitized ovens for accomplishing the same. In certain example embodiments, a unit is pre-heated to one or more intermediate temperatures, localized heating via at least one substantially two-dimensional array of heat sources is provided proximate to the peripheral edges of the unit so as to melt fits placed thereon, and cooled. In certain non-limiting implementations, the pre-heating and/or cooling may be provided in one or more steps. An oven for accomplishing the same may include multiple zones for performing the above-noted steps, each zone optionally including one or more chambers. Accordingly, in certain example embodiments, a temperature gradient proximate to the edges of the unit is created, thereby reducing the chances of breakage and/or at least some de-tempering of the substrates.