So i'm putting a bagel with cheese and ham on it into a conventional oven to toast it a bit. My end goal is for the cheese to be completely melted and the bagel not too crisp/dry.
What time and temperature combination is best for this?
Broiling would work, but if the bagel is cold and untoasted, you might want hotter all around. I recommend baking/top-rack/at 500 to get both effects. Given the vagaries of oven timing, I'd start with 5 minutes, checking at 3, just to be safe. Experimental, but tweak-able: If your cheese is not browning, go hotter. If your bagel is burning (but all else is well), lower the temp a bit, open the oven door, or switch to a straight broil.
P.S. Toaster/ovens are perfect for this, and probably worth the cost of admission for melting cheese alone.
To do this you want to apply heat to the cheese (to melt it) and not to the bagel (so it doesn't dry).
This is probably best achieved by grilling (broiling in the US) the bagel, rather than putting it in an oven, so the direct heat on the cheese melts it, but the bagel is not warmed so it doesn't crisp or dry.
This assumes you have an open bagel obviously. if you are have a closed bagel, with a top and a bottom, then I would melt the cheese on one half under the grill and the put the top piece on.
If you have to oven cook it then it's a trade off between high temp, which will crisp the bagel whilst the cheese is melting and the melting of the cheese should take a short time, or lower temp where the bagel is more likely to dry out as you need to leave it in for longer to get the melted cheese you want.