Will be joining my student in Madrid in July. Plan on going to Barcelona to return. Any itinerary suggestions for 1 week?

It's not much time. What are you really interested in doing?

I think you may find Maribel's Guide to Madrid and Barcelona helpful in planning your time.

http://mariblesguides.com

By a week do you mean 7 full days and nights? And is that to split between Madrid and Barcelona, or do you mean a week in Madrid, then go to Barcelona. If you have only one week total I'd do 4 nights Madrid, 3 Barcelona and while in Madrid I'd do a day trip to Toledo and one to Segovia and two days exploring Madrid itself. Then the rest of the time in Barcelona. If you meant you had an entire week in Madrid then I'd probably do a couple of days in Salamanca (overnight) and the other five days in Madrid with the two day trips.

I was in Madrid last July and did not find it unbearably hot - pleasantly hot maybe. If you have an air conditioned hotel to go back to for a couple of hours in the middle of the day you'll be fine unless you are really heat intolerant.

depends on your interest.
if you like museums, Madrid will take more than a day or two ( no time for side trips).
It is a huge city with huge traffic.
Barcelona is more relaxing, on the sea, many museums and galleries , but much easier to get around than Madrid.

Will have 4 days alone in Madrid then 3 days in Barcelona together.

Excellent suggestions about the day trips...just what I was thinking. How about a winery near Madrid?

From Madrid I would suggest day trips to Segovia and Toledo. Both are worth checking out, but it doesn't give you much time in Madrid itself, but depends how much you like large cities and all they have to offer. With only 3 days in Barcelona, I would suggest just staying there--it's a fabulous city and you won't run out of things to do in 3 days.