I went to Jordan end of March and I always needed a jacket and a scarf.
The summer months will definetely be too hot, maybe except the higher places like Amman and Jerash.
Winter can be quite cold, even snowy. If so, some places might be hard to access.
Downside of my piece of advise is that this time would be "high season".
Jordan is located in the Middle East.
So there is a lot of desert and the picture coming to your head being hot is true, at least partly.
But it is a dry heat. So very different to tropical climate.
interesting fact: Jordan's health system is earning more money than they spent!
which means the health system is really good. even for Western standards.
Since it is not a tropical country most of the nasty (tropical) diseases are not present.
Do like in many foreign countries:
Cook it, boil it, peel it or forget it!
Especially compared to the neighbouring countries Jordan is safe.
Even if you think of terror attacks, there have been very few in the history of Jordan.
The main issues will be pickpoeckts etc. as in all major places with tourists around.
I found Jordan not that easy, straight forward and cheap to travel.
Amman is well connected to many sights but that's about it.
Taxi is a really common mean of transportation even for travelling from one town to the other.
A rental car is another option,
Bus + Taxi or rental car
I took a mini bus from Amman.
Later a taxi from Petra.
Jordan was the first time I travelled to the Middle East.
You cannot compare it budget- wise to Asia or South America.
It is more expensive.
Sometimes I even felt it was more expensive than Europe because there is less choice.
So don't expect it to be cheap.
I didn't book anything in advance. And I made good experience with it.
The well known websites for accomodation etc work in Jordan perfectly.
Of course, there is PETRA. And it is great.
The whole area of Petra is much bigger than I expected it to be.
I hiked there about 8 hours!!!
There is Wadi Rum, a great desert area.
Go to see and "swim" in the Dead Sea. There is nothing like it.
If you are interested in history, there are a bunch of Biblical places.
So you see, there is a lot to do and see in Jordan!
One or two days in Amman are enough. There is not much to see. Maybe some museum or the amphitheater.
Must- see is Petra. Best, take your time there and visit it on two days. It is breathtaking and quite big.
From Petra you can go South to Wadi Rum and from there further South to Aqaba to enjoy the Red Sea.
On your way back to Amman you should go to and if you like, pass by some biblical places.
North of Amman and around there are some (supposed to be) interesting places like Jerash and the desert castles like Qasr el Amra.
As Amman is the starting point for many travellers, you might want to check out the free walking tour of Pasha Hotel. Of course, it is a hotel and there is a nice restaurant connected. You can also check out the facebook page.