New Mexico can get to 105 during the summer but usually its in the 90's. Lower elevations are hotter than higher elevations. For the past several years we spent our winters in Palm Springs area which gets up to 120 degrees in the summer so we always spent our summers in New Mexico.
Back in 1995 we went to NM for a 2 week vacation and before Christmas moved there. During the vacation we fell in love with the Land of Enchantment. We started full timing in 2005 and just left the road and bought a home just half hour south of Albuquerque. Most of the summer days will be 95 but with the low humidity its nice. A story that I always tell is that I was working in the back yard and worked up a sweat and went and sat under a shade tree and I started shivering, the sweat was evaporating so fast because of the 6% humidity that I was actually cold and it was 95 outside.
There are many RV parks in the state that will charge $600 or less. You may or may not get a swimming pool but if you do it's heaven when you can go get cooled off, if and when the temps reach 105 for a few days or up to a week. We consider 95 degrees here a nice day.
One thing that is definite is that we are missing the Palm Springs weather this winter. We wanted to stay in our 55+ Gated community this winter and see how it is. It's gets cold and some nights it gets down the teens but when the sun comes up it gets nice out. Right now in January most days are in the low to mid 50's. Next Dec-Jan- Feb we plan to get the RV out of our storage yard here in the community and enjoy Southern California.
Long post and keep checking the New Mexico RV parks and you'll find one that fits your budget. Maybe you'll fall in love with the Land of Enchantment like we did.