That's merely a reassertion of your conclusion; it's not a counterargument to Juma's rebuttal. He drew the obvious analogy with infinite space. So deal with his objection. Either (1) claim that space has to be finite too because if space were infinite we couldn't possibly be "here", or (2) explain what it is about time that makes the logic of time different from the logic of space, or (3) admit you don't have a justification for your assertion.
Even if you can't wrap your mind around that, we know that the universe would have subject to a heat death by now.
"Heat death" is an 1800s concept, based on an 1800s understanding of thermodynamics. Physicists at that time thought it was a fundamental law of physics that entropy always increases. And yet you can watch entropy decrease all by itself any time you please -- all you need is a drop of water, a bit of dust, and a microscope. It's called "Brownian motion" -- a dust particle that has been brought to rest by friction from a viscous fluid suddenly starts moving, in contravention of every principle of 1800s physics. Welcome to 1902. Thermodynamics is now understood to be an emergent phenomenon resulting from the statistics of large numbers of particles moving mostly independently of one another. Entropy decreases aren't impossible; it's just that a transition from a low-entropy state to a neighboring high-entropy state is more probable than the reverse transition; and big entropy decreases are vastly more improbable than tiny little entropy decreases, such as a dust particle accelerating.
The point is, vastly improbable is an entirely different beast from impossible. It just means a ridiculously long time can be expected to pass between one occurrence and the next. A ridiculously long time is a finite amount. So if time was infinite, then there has been enough time for arbitrarily large entropy decreases to have already happened, infinitely many times. Thermodynamics is therefore no obstacle to an eternal universe. If something resembling a "heat death" occurs, it will eventually reverse itself. Patience is a virtue.