I looked up your transformer. Although it works, the maximum current it can output at 8v is 1.25 amps. This means that with all the GI turned on, it must not pull more than 1.25 amps. You'd have to calculate how many bulbs (Leds?) you are driving and then calculate maximum current pulled. If it can exceed the 1.25A of the transformer to be safe you should use a bigger transformer.

Let's say every led bulb pulls 0.02 Amps or so, to reach 1.25vA you could power 62 Leds.

A transformer getting warm is normal. Warm, not hot. If you did things correctly you will have fused both sides of the transformer and avoid any risks possible.

10 VA is the 8VAC output of his transformer.

You seem pretty savvy, so what prevents you from using a second or more transformer and split the load?