PHB p153
"Stacking Effects: Spells that give bonuses or penalites to attack rolls, damage rolls, saving throws, and other attributes usually do not stack with themselves. For example, two bless spells don't give recipients twice the benefits of one bless.... more generally, two bonuses of the same type don't stack even if they come from different spells...In cases when two or more identical spells are operating in the same area, but at different strengths only the best one applies."
So in other words, they don't stack. There is one aid up at a given time. Each time an aid's temp hps are knocked out, it can be replaced with another aid (and more temp hps from that casting), but the total temp hps can never exceed the temp hps from a single casting.
Its the same as casting say haste. You can't cast multiple hastes to get +20 AC bonus and 5 extra actions. As a rule spells NEVER stack with themselves. Vampiric touch would only grant more temp hps if you did more damage than you currently had temp hps, though it could heal you multiple times if you were wounded (the instantaneous duration of the spell).
If a spell is in effect you cannot get more benefit from another casting, unless you roll higher (in the case of spells with variables) or the effect is instantaneous (as with healing spells).
Spells never stack with themselves, unless otherwise stated in the spell description.