i want to keep the chrome finish or slightly brown it. but iwant to do it cold not hot. any suggestions?
First, is the barrel chrome plated? If it is, it will not "take" a browning solution, be it hot or cold type because these all work by turning the steel/iron (not chrome) into ferric oxide.
On the other hand, if it is chrome plated, it doesn't need any further protection.
If you do not have a chrome plated barrel, the various brands of fluids will work.
The only commercially available "hot" browning I am aware of is Birchwood Caseys' Plum Brown. This is usually applied to a barrel which has been heated to about 280 degrees F.
The surface must be totally free of grease or oil (including the oil from your fingers when you touch it.)
I have not tried using this product cold, so I don't know what it would do.
It does contain mercury so don't handle it with your bare skin, and don't breath the fumes it gives off when it is applied to the hot surface.
If you would be content with a slightly irregular blue/black you could use one of the commercially available Instant Blueing products. There are several brands and they all seem to work. They will give fair to good protection to your barrel if you keep them oiled.