The main constraint with all titanium suppressors is keeping the temperature under 800 degrees F. Assuming you're shooting at a remotely reasonable rate of fire, I wouldn't anticipate any issues on a bolt action rifle. The titanium cans tend to cool pretty quickly. That said, I've never tried to get a temperature reading off of a hot suppressor. Testing with an IR thermometer would be interesting to my inner nerd. Both TB and Dead Air are very responsive (haven't dealt with Silencerco at all) so you could also try asking them directly. The newer Diligent Defense Enticers are getting good reviews as well, but I have no experience with them.
As far as my hunting suppressors go, I started with a Dead Air Sandman-S, which I don't really consider a "hunting" suppressor anymore. It's just too heavy and had too much impact on the balance of my rifle. It's now relegated to use on semi-autos. My hunting suppressor is now a Dead Air Nomad LT which, in addition to being much lighter than the Sandman, is much quieter as well. I also have a Thunderbeast Ultra 5 in NFA jail. The Nomad is set up to use the Thunderbeast CB mounts, so I'll have the ability to swap between those two suppressors on my .30 caliber and under hunting rifles. I expect that some point of impact shift will occur between the two and re-zeroing will be required, so that's not something I'd do in the field.
The plan for these two suppressors is to use the Nomad LT primarily on a 16.5" .308 bolt gun. The Ultra 5 will primarily be used on my 24" 6.5 PRC and a 22" .300 WM that I'm starting the build process on. Common mounts mean that I do maintain the ability to switch it up rather easily though.
For rimfire, I have a Dead Air Mask, which I'm very happy with. For the over-.30 crowd, I have a Rex Silentium MG7 in .458 in NFA jail as well. Hopefully both the MG7 and the Ultra 5 will be approved soon. I'm about 1 year into the wait for both of them. I think I'm done buying suppressors for a while, but they're highly addictive.