Merino tends to hold the moisture a little more than high quality synthetic base layers. However it also tends to be warmer when wet (I can vouch for this having ended up in a canal once!). Some riders swear by merino.
As indicated above, the issue maybe what’s over the base layer – most day packs don’t breath particularly well. Soft and hard shell jackets can also prevent moisture escaping. My soft shell jacket has a breathable section in the back for precisely this reason.
Jackets with pit vents can be very good. Zip off arms are even better allowing you to keep your core warm while allowing your arms to regulate your temperature. A gilet (soft or hard shell) is also excellent for this.
I tend to run pretty cool but would never jog with a merino base layer and polar fleece.
Layering allows you to adjust your clothing according to conditions and intensity of exercise. You could also try investing in day pack with better ventilation.