You don't necessarily feel more jazzed up by adding aspirin.
Supposedly and in pretty basic terms the salycilate (aspirin) is supposed to inhibit the negative feedback loop that would reduce beta agonist production.
It inhibits prostaglandin production and lengthens the effects.
It's not supposed to increase the thermogenic action (elevate temp) or provide more stimulatory effect, just prolong it a bit more.
Caffeines role amongst other things increase cAMP levels can be prolonged too by the use of processed grapefruit extract 'naragenin' which slow the rate that the hepatic system converts caffeine to para-xanthine.