AC is just not as prevalent in Europe as here. This past summer they had a really hot and humid summer and lack of AC seemed to be a problem for some people here who posted. It just all depends on how the weather goes, just like here.

Also - once you book a room, you can still keep looking when you get closer to your date. You might be able to get a good deal on a hotel that would generally be cheaper.

Lastminute.com or Eurocheap are two sites you could start to check around three weeks before your trip. Just make sure you dont incur cancellation fees if you book an earlier place.

Okay I finally think I found it. On my first trip to Paris I will be staying at Hôtel Résidence Monge has anyone stayed here? How much will it cost me to get there from the Train Station, I'll be coming in from London by the Eurostar?

Are you coming into Gare Nord on Eurostar? It would be a quick metro ride to Place Monge metro station.

A taxi might be about 20ish E depending on traffic in my guess.

Consider a bed and breakfast. There are folks in Paris who'll rent you a room or two in their homes or apartments, and give you breakfast, too, for well within your budget. I've never tried this, but I've spoken to some who have, and they recommended this unconventional approach enthusiastically. 'Alcoves et Agapes' is the agency, if I recall.