Radon mitigation vs slab temperature

I’m a builder in Montana. I’m selling a spec house that tested 5.5 and so I need to mitigate the radon down to below 4. The house is on a frost protected shallow foundation. My question is, wouldn’t putting in a radon fan pull cold air under the slab, potentially allowing the ground to freeze under the slab?
Alternatively I’m considering putting an HRV in because I think the home would benefit from it anyway. Has a tight blower door score.
Thanks
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Depends if your underslab assembly has access to daylight. To which a negative radon mitigation fan wouldn't really be needed anyway since it's ventilated.
If it's not, it would be sucking air from inside the house, whatever minor gaps.
If the radon number is high, I assume you don't have a vapour barrier under the slab. Or some considerable continuity issues.
You might find your numbers go down with just the HRV.
Jamie
You would need a stronger fan than a typical radon fan to pull enough air to make the under-floor space cold enough to change the temperature by more than a degree or two. Keep in mind that the earth's heat and indoor heat are both working against the cold air trying to freeze your soil.
There is anecdotal evidence of balanced ventilation systems reducing radon levels, but radon experts strongly recommend one of the many systems developed over many years and with millions of successful installations instead. You can read about those systems here: https://codes.iccsafe.org/content/IRC2021P1/appendix-af-radon-control-methods, or this is a more detailed alternative that's part of my state's building code: https://store.astm.org/e1465-08.html.
A typical radon exhaust fan is only going to be running around 250 CFM or so at most, and usually much less than that. There just isn't enough airflow to significantly alter the subsoil temperature, so you shouldn't have any additional freeze concerns.
Note that the point of a radon system under the slab (which is what I assume you're considering here) is to put the soil under the home at a slight negative pressure, so that all the radon "leaks" go into the radon system and get exhausted out of the home to the exterior. It's common practice to seal the slab to wall transition with these systems. The better sealed everything is, the lower the actual airflow through the radon system will be. You really only need the fan drawing air from the soil, any leaks to atmospheric air aren't helping things any from a radon mitigation standpoint.
Bill
Updating my post as I finished mitigating the radon. I decided to test out an HRV. I used a Fantech Hero120 HRV. The HRV has been running in low mode for 3 days now (70cfm). The house was closed up for that time period and is now reading 0.7 radon. I monitored this value about 3ft off the ground on the first level of the house.
I installed the HRV in the conditioned attic of this 2 story home. The stale air is pulled from a new duct added in the ceiling of the second story above the stairs. The fresh air is attached to the HVAC trunk line running to supply air to the first floor vents. Unfortunately my chase from 1st to second floor was full already. And I did not want to install on the air return of the HVAC system as then an interlock to the blower is required. That would use a significant amount of electricity since the HRV is going to run continually.
Thanks for the feedback on my concerns being unnecessary for the radon fan to cool down soil temp. I decided the HRV was a good path because the blower door score was tight and this install would solve likely solve two problems. And the results show it is working. Will bump it up to full speed 120CFM to see where that gets.